aarjaneiro/planetmath huggingface dataset:
table of division up to 12

table of division up to 12

In this table of

division

, the column operand is first and the row operand is second. For the sake of compactness, overlines have been used over repeating decimals when the operands are coprime to each other and to 10.

÷

1

2

3

4

5

6

7

8

9

10

11

12

1

1

0.5

0

.

3

¯

0.25

0.2

0.1

⁢

6

¯

0

.

142857

¯

0.125

0

.

1

¯

0.1

0

.

09

¯

0.08

⁢

3

¯

2

2

1

0

.

6

¯

0.5

0.4

0

.

3

¯

0

.

285714

¯

0.25

0

.

2

¯

0.2

0

.

18

¯

0.1

⁢

6

¯

3

3

1.5

1

0.75

0.6

0.5

0

.

428571

¯

0.375

0

.

3

¯

0.3

0

.

27

¯

0.25

4

4

2

1

.

3

¯

1

0.8

0

.

6

¯

0

.

571428

¯

0.5

0

.

4

¯

0.4

0

.

36

¯

0

.

3

¯

5

5

2.5

1

.

6

¯

1.25

1

0.8

⁢

3

¯

0.714285

0.625

0.5

0.5

0.45

0.41

⁢

6

¯

6

6

3

2

1.5

1.2

1

0

.

857142

¯

0.75

0

.

6

¯

0.6

0

.

54

¯

0.5

7

7

3.5

2

.

3

¯

1.75

1.4

1.1

⁢

6

¯

1

0.875

0

.

7

¯

0.7

0

.

63

¯

0.58

⁢

3

¯

8

8

4

2

.

6

¯

2

1.6

1

.

3

¯

1

.

142857

¯

1

0

.

8

¯

0.8

0

.

72

¯

0

.

6

¯

9

9

4.5

3

2.25

1.8

1.5

1

.

285714

¯

1.125

1

0.9

0

.

81

¯

0.75

10

10

5

3

.

3

¯

2.5

2

1

.

6

¯

1

.

428571

¯

1.25

1

.

1

¯

1

0

.

90

¯

0.8

⁢

3

¯

11

11

5.5

3

.

6

¯

2.75

2.2

1.8

⁢

3

¯

1

.

571428

¯

1.375

1

.

2

¯

1.1

1

0.91

⁢

6

¯

12

12

6

4

3

2.4

2

1

.

714285

¯

1.5

1

.

3

¯

1.2

1

.

09

¯

1

The longest northwest to southeast diagonal obviously contains ones.

Title

table of division up to 12

Canonical

name

TableOfDivisionUpTo12

Date of creation

2013-03-22 16:36:16

Last modified on

2013-03-22 16:36:16

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Data Structure

Classification

msc 00A06

Classification

msc 12E99

Classification

msc 00A05

Generated on Tue Feb 6 22:19:23 2018 by

LaTeXML
table of multiplication up to 12

table of multiplication up to 12

Because of the commutative property of

multiplication

, it does not matter if the row or the column gives the first operand.

×

1

2

3

4

5

6

7

8

9

10

11

12

1

1

2

3

4

5

6

7

8

9

10

11

12

2

2

4

6

8

10

12

14

16

18

20

22

24

3

3

6

9

12

15

18

21

24

27

30

33

36

4

4

8

12

16

20

24

28

32

36

40

44

48

5

5

10

15

20

25

30

35

40

45

50

55

60

6

6

12

18

24

30

36

42

48

54

60

66

72

7

7

14

21

28

35

42

49

56

63

70

77

84

8

8

16

24

32

40

48

56

64

72

80

88

96

9

9

18

27

36

45

54

63

72

81

90

99

108

10

10

20

30

40

50

60

70

80

90

100

110

120

11

11

22

33

44

55

66

77

88

99

110

121

132

12

12

24

36

48

60

72

84

96

108

120

132

144

Obviously the longest northwest to southeast diagonal contains numbers of the form

n

2

.

Title

table of multiplication up to 12

Canonical

name

TableOfMultiplicationUpTo12

Date of creation

2013-03-22 16:36:14

Last modified on

2013-03-22 16:36:14

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Data Structure

Classification

msc 00A06

Classification

msc 00A05

Classification

msc 11B25

Generated on Tue Feb 6 22:19:25 2018 by

LaTeXML
therefore sign

therefore sign

The

therefore sign

“

∴

” is used especially in handwritten mathematical text as a shorthand of the or

relations

:

S

1

∴

S

2

It expresses that

S

2

has been inferred from

S

1

or from

S

1

and some preceding facts. The sign is rather a punctuation mark than a symbol of

logical implication

. Grammatically, it could be characterised a conclusive coordinating . The usage of the symbol is not mathematically

well-defined

, and it often means ‘we can conclude in

context

’ or ‘we can conclude from statements already shown or assumed to be true’.

For example, in determining an angle of a

right triangle

, one may write

sin

α

=

1

2

∴

α

=

30

∘

Here, “

∴

” does not a proper

implication

“

⇒

”, since the exact implication here would be

sin

⁡

α

=

1

2

⇐

α

=

30

∘

.

To obtain a strict implication, we would need to introduce some of the context.
For

instance

, we know that, since

α

is an angle of a right triangle,

0

∘

≤

α

≤

90

∘

,
so what we wrote could be interpreted as the implication

sin

⁡

α

=

1

2

∧

0

∘

≤

α

≤

90

∘

⇒

α

=

30

∘

.

Title

therefore sign

Canonical

name

ThereforeSign

Date of creation

2013-03-22 17:55:51

Last modified on

2013-03-22 17:55:51

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

8

Author

pahio (2872)

Entry type

Definition

Classification

msc 00A06

Classification

msc 00A05

Related topic

RingsOfRationalNumbers

Related topic

LogarithmicScale

Generated on Tue Feb 6 22:19:27 2018 by

LaTeXML
Nesbitt’s inequality

Nesbitt’s inequality

Nesbitt’s

inequality

says, that for positive real

a

,

b

and

c

we have:

a

b

+

c

+

b

a

+

c

+

c

a

+

b

≥

3

2

.

This is a special case of Shapiro’s inequality.

Title

Nesbitt’s inequality

Canonical name

NesbittsInequality

Date of creation

2013-03-22 12:36:59

Last modified on

2013-03-22 12:36:59

Owner

mathwizard (128)

Last modified by

mathwizard (128)

Numerical id

7

Author

mathwizard (128)

Entry type

Theorem

Classification

msc 00A07

Related topic

ShapiroInequality

Generated on Tue Feb 6 22:19:28 2018 by

LaTeXML
proof of Nesbitt’s inequality

proof of Nesbitt’s inequality

Starting from Nesbitt’s

inequality

a

b

+

c

+

b

a

+

c

+

c

a

+

b

≥

3

2

we transform the left hand side:

a

+

b

+

c

b

+

c

+

a

+

b

+

c

a

+

c

+

a

+

b

+

c

a

+

b

-

3

≥

3

2

.

Now this can be transformed into:

(

(

a

+

b

)

+

(

a

+

c

)

+

(

b

+

c

)

)

⁢

(

1

a

+

b

+

1

a

+

c

+

1

b

+

c

)

≥

9

.

Division by 3 and the right yields:

(

a

+

b

)

+

(

a

+

c

)

+

(

b

+

c

)

3

≥

3

1

a

+

b

+

1

a

+

c

+

1

b

+

c

.

Now on the left we have the

arithmetic mean

and on the right the

harmonic mean

, so this inequality is true.

Title

proof of Nesbitt’s inequality

Canonical name

ProofOfNesbittsInequality

Date of creation

2013-03-22 12:37:01

Last modified on

2013-03-22 12:37:01

Owner

mathwizard (128)

Last modified by

mathwizard (128)

Numerical id

6

Author

mathwizard (128)

Entry type

Proof

Classification

msc 00A07

Generated on Tue Feb 6 22:19:30 2018 by

LaTeXML
cabtaxi number

cabtaxi number

A

cabtaxi number

for a given

n

is the smallest positive number which can be written as

a

3

+

b

3

in

n

different ways, with either

a

or

b

allowed to be negative integers. For example, 91 is the 2nd cabtaxi number since it can be expressed

(

-

5

)

3

+

6

3

=

3

3

+

4

3

=

91

. The known cabtaxi numbers are 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, listed in A047696 of Sloane’s OEIS. Adding the

restriction

a

≥

b

>

0

gives the

definition

for the

taxicab numbers

.

Title

cabtaxi number

Canonical

name

CabtaxiNumber

Date of creation

2013-03-22 17:56:08

Last modified on

2013-03-22 17:56:08

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 00A08

Generated on Tue Feb 6 22:19:32 2018 by

LaTeXML
large integers that are or might be the smallest of their kind

large integers that are or might be the smallest of their kind

For the purpose of this feature, the arbitrary cutoff is

10

7

.

19099919

is the smallest prime to start a

Cunningham chain

of length 8.

85864769

is the smallest prime to start a Cunningham chain of length 9.

545587687

is the smallest class 13+ prime in the

Erdos-Selfridge classification of primes

.

635318657

is the smallest number that can be expressed as a sum of two

fourth powers

in two different ways.

823766851

is the smallest prime with

primitive root

48.

906150257

is the smallest

counterexample

to Pólya’s

conjecture

.

1023456789

is the smallest

pandigital number

in base 10.

1704961513

is the smallest class 14+ prime in the Erdős-Selfridge classification of primes.

10123457689

is the smallest pandigital prime in base 10.

26089808579

is the smallest prime to start a Cunningham chain of length 10.

665043081119

is the smallest prime to start a Cunningham chain of length 11.

554688278429

is the smallest prime to start a Cunningham chain of length 12.

10

13

+

1

is, as of 2005, the smallest candidate for a counterexample to the

Mertens conjecture

(though the smallest counterexample could turn out to be as large as

3.21

×

10

64

).

4090932431513069

is the smallest prime to start a Cunningham chain of length 13.

95405042230542329

is the smallest prime to start a Cunningham chain of length 14.

810433818265726529159

is the smallest prime known to start a Cunningham chain of length 16, but there could be a smaller such prime.

439351292910452432574786963588089477522344721

is the smallest prime in Paul Hoffman’s erroneous version of Wilf’s

primefree sequence

in which

a

1

=

3794765361567513

,

a

2

=

20615674205555510

and

a

n

=

a

n

-

2

+

a

n

-

1

for

n

>

2

.

If an odd perfect number exists, it is at least

10

300

+

1

.

Title

large

integers

that are or might be the smallest of their kind

Canonical

name

LargeIntegersThatAreOrMightBeTheSmallestOfTheirKind

Date of creation

2013-03-22 16:04:14

Last modified on

2013-03-22 16:04:14

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

15

Author

Mravinci (12996)

Entry type

Feature

Classification

msc 00A08

Related topic

SmallIntegersThatAreOrMightBeTheLargestOfTheirKind

Generated on Tue Feb 6 22:19:36 2018 by

LaTeXML
taxicab numbers

taxicab numbers

The number

1729

has a reputation of its own. The reason is the famous exchange between

http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Hardy.html

G. H. Hardy, a famous British mathematician (1877-1947), and

http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Ramanujan.html

Srinivasa Ramanujan , one of India’s greatest mathematical geniuses (1887-1920):

In 1917, during one visit to Ramanujan in a hospital (he was ill for much of his last three years), Hardy mentioned that the number of the taxi cab
that had brought him was

1729

, which, as numbers go, Hardy thought
was “rather a dull number”. At this, Ramanujan perked up, and said
“No, it is a very interesting number; it is the smallest number
expressible as a sum of two cubes in two different ways.”

Indeed:

1729

=

1

+

12

3

=

9

3

+

10

3

.

Moreover, there are other reasons why

1729

is far from dull.

1729

is the third

Carmichael number

. Even more strange, beginning at the

1729

th decimal digit of the transcental number

e

, the next ten
successive digits of

e

are 0719425863. This is the first appearance
of all ten digits in a row without repititions.

More generally, the smallest

natural number

which can be expressed as the sum of

n

positive

cubes is called the

n

th

taxicab number

. The first taxicab numbers are:

2

=

1

3

+

1

3

,

1729

=

1

3

+

12

3

=

9

3

+

10

3

,

87539319

=

167

3

+

436

3

=

228

3

+

423

3

=

255

3

+

414

3

followed by

6963472309248

(found by E. Rosenstiel, J.A. Dardis, and C.R. Rosenstiel in 1991) and

48988659276962496

(found by David Wilson on November 21st, 1997).

Title

taxicab numbers

Canonical

name

TaxicabNumbers

Date of creation

2013-03-22 15:43:00

Last modified on

2013-03-22 15:43:00

Owner

alozano (2414)

Last modified by

alozano (2414)

Numerical id

6

Author

alozano (2414)

Entry type

Feature

Classification

msc 00A08

Generated on Tue Feb 6 22:19:40 2018 by

LaTeXML
canonical

canonical

A mathematical object is said to be

canonical

if it arises in a natural way without introducing any additional objects.

Examples

1.

Suppose

A

×

B

is the

Cartesian product

of sets

A

,

B

.
Then

A

×

B

has two

A

×

B

→

A

and

A

×

B

→

B

defined in a natural way. Of course, if
we assume more

structure

of

A

,

B

there are also other

projections

.

2.

http://planetmath.org/CanonicalProjection

canonical projection

(in

group theory

)

Notes

For a discussion of the theological use of canonical, see

[

1

]

.

References

1

Wikipedia, article on

http://en.wikipedia.org/wiki/Canonical

canonical.

Title

canonical

Canonical name

Canonical

Date of creation

2013-03-22 14:44:32

Last modified on

2013-03-22 14:44:32

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

6

Author

mathcam (2727)

Entry type

Definition

Classification

msc 00A20

Related topic

CanonicalFormOfElementOfNumberField

Generated on Tue Feb 6 22:19:45 2018 by

LaTeXML
completing the square

completing the square

Let us consider the

expression

x

2

+

x

⁢

y

, where

x

and

y

are real (or

complex

) numbers.
Using the

formula

(

x

+

y

)

2

=

x

2

+

2

⁢

x

⁢

y

+

y

2

we can write

x

2

+

x

⁢

y

=

x

2

+

x

⁢

y

+

0

=

x

2

+

x

⁢

y

+

y

2

4

-

y

2

4

=

(

x

+

y

2

)

2

-

y

2

4

.

This manipulation is called

completing the square

[

1

]

in

x

2

+

x

⁢

y

, or completing the square

x

2

.

Replacing

y

by

-

y

, we also have

x

2

-

x

⁢

y

=

(

x

-

y

2

)

2

-

y

2

4

.

Here are some applications of this method:

•

http://planetmath.org/DerivationOfQuadraticFormula

Derivation

of the solution formula to the

quadratic equation

.

•

Putting the general equation of a circle, ellipse, or hyperbola into standard form, e.g. the circle

x

2

+

y

2

+

2

⁢

x

+

4

⁢

y

=

5

⇒

(

x

+

1

)

2

+

(

y

+

2

)

2

=

10

,

from which it is frequently easier to read off important information (the center, radius, etc.)

•

Completing the square can also be used to find the extremal value
of a quadratic polynomial

[

2

]

without

calculus

.
Let us illustrate this for the

polynomial

p

⁢

(

x

)

=

4

⁢

x

2

+

8

⁢

x

+

9

.
Completing the square yields

p

⁢

(

x

)

=

(

2

⁢

x

+

2

)

2

-

4

+

9

=

(

2

⁢

x

+

2

)

2

+

5

≥

5

,

since

(

2

⁢

x

+

2

)

2

≥

0

. Here, equality holds if and
only if

x

=

-

1

.
Thus

p

⁢

(

x

)

≥

5

for all

x

∈

ℝ

, and

p

⁢

(

x

)

=

5

if and only if

x

=

-

1

.
It follows that

p

⁢

(

x

)

has a

global minimum

at

x

=

-

1

, where

p

⁢

(

-

1

)

=

5

.

•

Completing the square can also be used as an

integration technique

to

integrate

, for example the

function

1

4

⁢

x

2

+

8

⁢

x

+

9

[

1

]

.

References

1

R. Adams,

Calculus, a

complete

course

,
Addison-Wesley Publishers Ltd, 3rd ed.

2

Matematiklexikon

(in Swedish),
J. Thompson, T. Martinsson, Wahlström & Widstrand, 1991.

(Anyone has an English reference?)

Title

completing the square

Canonical

name

CompletingTheSquare

Date of creation

2013-03-22 13:36:27

Last modified on

2013-03-22 13:36:27

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

14

Author

mathcam (2727)

Entry type

Algorithm

Classification

msc 00A20

Related topic

SquareOfSum

Generated on Tue Feb 6 22:19:48 2018 by

LaTeXML
counterexample

counterexample

A

counterexample

is an example which is used to prove that a statement is false.

For instance, to disprove that the statement “For all

n

,

2

2

n

+

1

is prime.”, one could exhibit

5

as a counterexample; since

2

2

5

+

1

=

641

×

6700417

, the statement is false.

Title

counterexample

Canonical

name

Counterexample

Date of creation

2013-03-22 14:43:00

Last modified on

2013-03-22 14:43:00

Owner

rspuzio (6075)

Last modified by

rspuzio (6075)

Numerical id

5

Author

rspuzio (6075)

Entry type

Definition

Classification

msc 00A20

Generated on Tue Feb 6 22:19:49 2018 by

LaTeXML
digital object

digital object

A

digital object

in a digital library is the textual or multimedia data and the metadata.

Formally, a digital object

D

⁢

O

is a quadruple

(

h

,

S

⁢

M

,

S

⁢

T

,

S

⁢

S

)

where

1.

h

∈

H

, where

H

is a set of universally unique handles (labels);

2.

S

⁢

M

=

{

s

⁢

m

1

,

s

⁢

m

2

,

…

,

s

⁢

m

n

}

is a set of streams;

3.

S

⁢

T

=

{

s

⁢

t

1

,

s

⁢

t

2

,

…

,

s

⁢

t

m

}

is a set of structural metadata

specifications

; and

4.

S

⁢

S

=

{

s

⁢

t

⁢

s

⁢

m

1

,

s

⁢

t

⁢

s

⁢

m

2

,

…

,

s

⁢

t

⁢

s

⁢

m

p

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is a set of Structured Streams functions defined from the streams in

S

⁢

M

and from the

structures

in

S

⁢

T

.

Title

digital object

Canonical

name

DigitalObject

Date of creation

2013-03-22 15:30:38

Last modified on

2013-03-22 15:30:38

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

11

Author

CWoo (3771)

Entry type

Definition

Classification

msc 00A20

Generated on Tue Feb 6 22:19:51 2018 by

LaTeXML
famous open questions in mathematics

famous open questions in mathematics

Despite the fact that at least a generation of mathematicians has tried to solve these problems, they still remain open:

1.

Goldbach conjecture

2.

Twin prime conjecture

3.

Poincaré

conjecture

4.

Riemann Hypothesis

5.

Birch and Swinnerton-Dyer conjecture

6.

P vs NP problem

7.

Hodge conjecture

8.

Solution to the Navier-Stokes equations

9.

Collatz problem

10.

Schanuel’s conjecture

11.

Beal conjecture

12.

Irrationality of Euler’s

constant

γ

13.

Existence

of an odd perfect number

14.

Koethe conjecture

15.

Invariant subspace problem

16.

Lehmer’s conjecture

Open problems

3 to 8, together with the quest for a

mathematical foundation

explaining the mass gap

property

in Yang-Mills theory, constitute a

collection

of problems known as the

Millennium Problems

. Please see

http://www.claymath.org/millennium/

http://www.claymath.org/millennium/ for more detail.

Note:

A mathematical foundation for the partial solution of the the mass gap property in Yang-Mills theory has been published by G. Cleaver and K. Tanaka (2000): “Ratio of Quark Masses in Duality Theories.”,

http://arxiv.org/abs/hep-th/0002089v1

on line, and can be accessed as a

http://arxiv.org/PS_cache/hep-th/pdf/0002/0002089v1.pdf

PDF file .

Title

famous open questions in mathematics

Canonical

name

FamousOpenQuestionsInMathematics

Date of creation

2013-03-22 14:42:52

Last modified on

2013-03-22 14:42:52

Owner

rspuzio (6075)

Last modified by

rspuzio (6075)

Numerical id

15

Author

rspuzio (6075)

Entry type

Example

Classification

msc 00A20

Related topic

TwoGeneratorProperty

Related topic

MillenniumProblems

Generated on Tue Feb 6 22:19:53 2018 by

LaTeXML
obvious

obvious

Mathematicians use phrases like “it is obvious that”, “it is easy to see that”, “it is clear that”, and “is

trivial

” to indicate that some steps have been omitted. The use of such

language

may be classified under three headings — honest, dishonest, and pedagogical.

The honest use of these phrases occurs when only a few steps have been omitted and these steps are simple enough that the average reader can easily fill in the gaps. Omitting such steps can be beneficial because it cuts down the length of an exposition and keeps the main ideas from getting lost amidst a morass of boring details and routine

operations

. By reminding the reader of small omissions in an unobtrusive fashion, such phrases help put the reader at ease — if they are left out, it is easy for the reader to be thrown off-course by a missing step or be left with an uneasy feeling that there might be a hole in a proof.

The dishonest use of these phrases occurs when a somewhat lengthy calculation has been left out because the author was too lazy to write it down. By using these phrases, the author hopes to intimidate potential critics from pointing out that material is missing by insinuating that anyone who would point out that something is missing is too stupid to fill in a few obvious steps. Frequent dishonest use of these terms may be a symptom of mathematheosis.

The pedagogical use of these phrases occurs when the author has deliberately left the filling-in of missing steps as an exercise to the reader.

Title

obvious

Canonical name

Obvious

Date of creation

2013-03-22 14:43:42

Last modified on

2013-03-22 14:43:42

Owner

rspuzio (6075)

Last modified by

rspuzio (6075)

Numerical id

10

Author

rspuzio (6075)

Entry type

Definition

Classification

msc 00A20

Synonym

easy to see

Synonym

clear

Generated on Tue Feb 6 22:20:02 2018 by

LaTeXML
On-Line Encyclopedia of Integer Sequences

On-Line Encyclopedia of Integer Sequences

An Internet

database

of

sequences

of

integers

, together with formulas,

generating functions

,

computer

programs

, keywords and cross-references to other sequences. Sometimes referred to by its acronym,

OEIS

. It was started by Neil Sloane as an outgrowth of his printed catalogs of

integer sequences

.

Each sequence is assigned a unique identification number (the letter A followed by six digits in base 10) based on the date of its

addition

to the database, though most entries contain information on their lexicographic

context

. In 2010 the database had almost 200000 sequences.

The most important sequences are tagged with the keyword “core.” Sequences of

fractions

are split into two sequences (numerators and denominators), while important mathematical constants like e are split into their base 10 digits. Zero is sometimes used as a placeholder value for non-existent terms.

A few other important keywords include: “frac” for most fractions, “cofr” for

continued fractions

, “eigen” for eigenvalues, “mult” for multiplicative sequences, “walk” for sequences pertaining to self-avoiding paths, etc.

The sequences included in the database range in subject from Sloane’s love of

combinatorics

to

number theory

, geometry, calculus,

cryptography

, quantum physics, etc., as well as many subjects that would seem to be far removed from mathematics, like archaeology and psychiatry.

In 2010 there was an effort to move the whole database to a Wiki platform, but this ultimately abandoned in favor of a custom-designed platform with a more rigorous editorial control. However, the OEIS does have a Wiki for subsidiary pages.

http://oeis.org/

The

On-Line Encyclopedia of Integer Sequences

References

1

A. Del Arte, “

http://www.southend.wayne.edu/modules/news/article.php?storyid=553

Mathematician reaches 100k milestone of online integer archive”

The South End

(Detroit), 11 Nov., Wayne State University (2004)

2

V. Origlio, “L’Enciclopedia delle sequenze intere”

Biblioteche Oggi

, Jan.-Feb. (2006): 41 - 45

Title

On-Line Encyclopedia of Integer Sequences

Canonical

name

OnLineEncyclopediaOfIntegerSequences

Date of creation

2013-03-22 15:47:36

Last modified on

2013-03-22 15:47:36

Owner

CompositeFan (12809)

Last modified by

CompositeFan (12809)

Numerical id

11

Author

CompositeFan (12809)

Entry type

Definition

Classification

msc 00A20

Synonym

OEIS

Synonym

Online Encyclopedia of Integer Sequences

Generated on Tue Feb 6 22:20:04 2018 by

LaTeXML