Lychrel number
Other bases
In base 2, 10110 (22 in decimal) has been proven to be a Lychrel number, since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after 4n steps it reaches a number consisting of 10, followed by n+1 ones, followed by 01, followed by n+1 zeros.

Lychrel number

Section Title: Other bases
Table Section Text: In base 2, 10110 (22 in decimal) has been proven to be a Lychrel number, since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after 4n steps it reaches a number consisting of 10, followed by n+1 ones, followed by 01, followed by n+1 zeros.

b	Smallest possible Lychrel number in base b written in base b (base 10)

2	10110 (22)

3	10201 (100)

4	3333 (255)

5	10313 (708)

6	4555 (1079)

7	10513 (2656)

8	1775 (1021)

9	728 (593)

10	196 (196)

11	83A (1011)

12	179 (237)

13	CCC (2196)

14	1BB (361)

15	1EC (447)

16	19D (413)

17	B6G (3297)

18	1AF (519)

19	HI (341)

20	IJ (379)

21	1CI (711)

22	KL (461)

23	LM (505)

24	MN (551)

25	1FM (1022)

26	OP (649)

27	PQ (701)

28	QR (755)

29	RS (811)

30	ST (869)

Sentence(s)

In base ten, Lychrel number includes 196.

final_sentence: In base ten, Lychrel number includes 196.