OpenLLM-France/wikimedia huggingface dataset:
# Fractal sequence

In mathematics, a fractal sequence is one that contains itself as a proper subsequence. An example is
       1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, ...
If the first occurrence of each n is deleted, the remaining sequence is identical to the original. The process can be repeated indefinitely, so that actually, the original sequence contains not only one copy of itself, but rather, infinitely many.

## Definition

The precise definition of fractal sequence depends on a preliminary definition: a sequence x = (x$_n$) is an infinitive sequence if for every i,
       (F1) x$_n$ = i for infinitely many n.
Let a(i,j) be the jth index n for which x$_n$ = i. An infinitive sequence x is a fractal sequence if two additional conditions hold:
       (F2) if i+1 = x$_n$, then there exists m < n such that
          $i=x_{m}$
       (F3) if h < i then for every j there is exactly one k such that
          $a(i,j)<a(h,k)<a(i,j+1).$
According to (F2), the first occurrence of each i > 1 in x must be preceded at least once by each of the numbers 1, 2, ..., i-1, and according to (F3), between consecutive occurrences of i in x, each h less than i occurs exactly once.

## Example

Suppose θ is a positive irrational number. Let
       S(θ) = the set of numbers c + dθ, where c and d are positive integers
and let
       c$_n$(θ) + θd$_n$(θ)
be the sequence obtained by arranging the numbers in S(θ) in increasing order. The sequence c$_n$(θ) is the signature of θ, and it is a fractal sequence.
For example, the signature of the golden ratio (i.e., θ = (1 + sqrt(5))/2) begins with
       1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, ...
and the signature of 1/θ = θ - 1 begins with
       1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, ...
These are sequences OEIS: A084531 and OEIS: A084532 in the On-Line Encyclopedia of Integer Sequences, where further examples from a variety of number-theoretic and combinatorial settings are given.
# John Graham Haggart

John Graham Haggart, PC (November 14, 1836 – March 13, 1913) was a Canadian politician.
Haggart served as a Member of Parliament from 1872 to 1913. This forty-year period of service in the Commons is the second-longest in Canadian history, exceeded only by Wilfrid Laurier, whose period of service (1874-1919) mostly overlaps with Haggart's. He was appointed as Postmaster General, serving in the cabinets of John A. Macdonald and John Abbott until 1892, when he switched portfolios, serving as Minister of Railways and Canals until the defeat of the Conservative government in 1896.
Prior to being elected to the House of Commons, Haggart was elected Mayor of Perth, Ontario three times: in 1867, 1869 and 1871.
There is a John Haggart fonds at Library and Archives Canada.
# Villy

Villy may refer to the following places:
* in France:
** Villy, Ardennes, in the Ardennes département
** Villy, Yonne, in the Yonne département
** Villy Bocage, in the Calvados département
** Villy-en-Auxois, in the Côte-d'Or département
** Villy-en-Trodes, in the Aube département
** Villy-le-Bois, in the Aube département
** Villy-le-Bouveret, in the Haute-Savoie département
** Villy-le-Maréchal, in the Aube département
** Villy-le-Moutier, in the Côte-d'Or département
** Villy-le-Pelloux, in the Haute-Savoie département
** Villy lez Falaise, in the Calvados département
** Villy-sur-Yères, in the Seine-Maritime département
* Villy, Burkina Faso, a town in central Burkina Faso
# Five A Day (video game)

Five A Day is multidirectional shooter for iOS devices developed by Jeff Minter and Ivan Zorzin of Llamasoft and published via the Apple App Store. The game is a redevelopment of one of Minter's first attempts at iOS programming, and is loosely based on Time Pilot. Although it does not explicitly announce itself to be a Minotaur Project game, the distinctive font and coloration of the text appearing throughout the game is that of the Commodore 64. The game's title is taken from the 5 A Day healthy eating program.

## Gameplay

The player controls a spaceship which remains in the centre of the screen while the game environment scrolls around it. The ship fires continuously in the direction it is pointing, with its bullets remaining in the coordinate system of the screen rather than the environment. The objective is for the player to shoot down enemy ships without colliding with them. Certain enemy ships will be using tractor beams to tow fruit, vegetables, and occasionally minotaurs behind them. Destroying these enemies will free the carried item allowing the player's ship to collect it. Collected items form a chain behind the spaceship, and these items can deal damage to enemies they hit. If enemies carrying items are not destroyed in time, they will pull the carried items in, which causes them to turn green and gain extra attacking power.
When a sufficient number of enemies are destroyed, a boss appears; a single enemy which fires a large number of bullets and is usually resistant to the ship's own bullets while being vulnerable to the trail of fruit. Once the boss is destroyed, the player moves on to the next stage.
Each game level is represented as a "day" and is divided into five stages: Haytime (Breakfast, referring to the feeding of sheep), Crunchtime (Work, referring to the Crunch Time experienced by game programmers), Nicecupofteatime (Tea break), Currytime (Dinner), and Sheepenumerationtime (Night, a reference to Counting sheep). Provided at least one fruit is collected from each of the five stages on a day, a "5 a day bonus" of an extra life is awarded. If any stage is completed with no fruit collected, the extra life cannot be awarded for that day. This produces the message "Fruitless - you've lost your way to five a day!", a reference to a slogan frequently used by the 5 A Day healthy eating promotions.

## Reception

Five A Day received positive reviews from Pocket Gamer, Arcadelife, and Kill Screen.
# Klostersee (Lehnin)

Klostersee (Lehnin) is a lake in Brandenburg, Germany. At an elevation of 29 m, its surface area is 0.38 km². It is located in the municipality of Kloster Lehnin, Potsdam-Mittelmark district.
# Eckard Rabe

Eckard Rabe is a former South African film, television and theatre actor. He is now a teacher at Parktown Boys' High School. He was born in 1948 in St Winifreds, Natal and grew up in Port Shepstone. He acted as the business tycoon and patriarch of the Edwards family on the local soap opera, Egoli - Place of Gold from 1995 to 2009. He has one daughter, Caitlin Bianca, by actress Jo Da Silva.

## Filmography

* Ballade vir 'n Enkeling (2015)
* Getroud met Rugby: Die Onvertelde Storie (2011)
* Catch a Fire (2006)
* Act of Piracy (1990)
* American Ninja 3: Blood Hunt (1989)
* Paradise Road (1988)
* Kampus: 'n Varsity-Storie (1986)
* Plekkie in die son (1979)
* Springbok (1976)
* Daar Kom Tant Alie (1976)
* Dog Squad (1973)

## Television

* 7de Laan (2010)
* Wild at Heart (2010)
* Egoli: Place of Gold (1995–2009)
* Westgate (1981)
* The Dingleys (1977)

## Teacher

Eckard Rabe is now an English teacher at Parktown Boys' High School
# William Cockburn (footballer)

William Cockburn (born 1889) was an English footballer who played as a defender for Liverpool in The Football League. Cockburn started his career at Rosehill before he moved to Stockport County F.C. He signed for Liverpool in 1924 and appeared 18 times during his debut season. He became a regular in the team the following season as he cemented a place in the Liverpool defence and only missed six of the 42 league matches during the season. He only appeared 9 times the following season and he was transferred to Queens Park Rangers F.C. in 1928.
# Vriesea clausseniana

Vriesea clausseniana is a plant species of flowering plant in the Bromeliaceae family. It is endemic to Brazil.
# Vriesea chrysostachys

Vriesea chrysostachys is a plant species in the genus Vriesea. It is an epiphyte native to Colombia, Peru, and Trinidad.

## Cultivars

* Vriesea 'Pactole'
# Heinrich von Virneburg

Henry III von Virneburg (c. 1295 – December 21, 1353) was Archbishop and Elector of Mainz (1328/37–1346/53).

## Life

Henry was a son of Count Ruprecht II of Virneburg and his wife Kunigunde of Neuenahr and a nephew of the archbishop of Cologne, Henry of Virneburg. It was his uncle's influence with Pope John XXII that determined the papal appointment for Henry as Archbishop of Mainz.

### Archbishop

The Mainz cathedral chapter had elected Archbishop Balduin of Luxembourg from Trier to succeed the deceased Matthias von Buchegg, with whom Heinrich fought a bitter dispute over the archiepiscopate of Mainz until 1336. Only then was he generally accepted.
Following Pope John XXII's death, Heinrich became a supporter of Emperor Ludwig of Bavaria. This created tensions with Pope Benedict XII. In 1338 a provincial synod took place in Mainz, at which he wanted to mediate between the pope and the emperor. Heinrich wrote a declaration to the Curia on March 27, 1338, but the attempt at mediation failed. During the Thuringian Counts' War, he supported the Counts fighting against the Wettins.
On 7 April 1346, Henry, because of his partisanship with Emperor Louis IV, was deposed by Pope Clement VI. The same day, Clemens appointed Gerlach von Nassau as the new archbishop of Mainz. After the death of Emperor Ludwig the following year, Heinrich's importance declined. Nevertheless, he maintained his position in Mainz until his death in 1353, mainly thanks to the active support of his cathedral provost Kuno II von Falkenstein, in constant disputes with Gerlach von Nassau. Heinrich was buried in Mainz Cathedral.
# Hello Sunshine

Hello Sunshine may refer to:
* "Hello Sunshine" (Super Furry Animals song)
* "Hello Sunshine" (Bruce Springsteen song)
* Hello Sunshine (book), a collection of poems and short stories by Ryan Adams
* Hello Sunshine (company), an American media company founded by actress Reese Witherspoon
# Adelpherupa lialuiensis

Adelpherupa lialuiensis is a moth in the family Crambidae. It was described by Koen V. N. Maes in 2002. It is found in Zambia.
# Vrátkov

Vrátkov is a municipality and village in Kolín District in the Central Bohemian Region of the Czech Republic. It has about 300 inhabitants.
# William Dobson (disambiguation)

William Dobson was an English Baroque painter of the 17th century.
William Dobson may also refer to:
* William Dobson (academic) (1650–1731), English academic, President of Trinity College, Oxford
* William Polk Dobson (1793–1846), American politician, state senator for Surry County, North Carolina
* William Charles Thomas Dobson (1817–1898), English painter
* William Dobson (antiquary) (1820–1884), English journalist and antiquary
* William Lambert Dobson (1833–1898), Australian judge and politician
* William J. Dobson (born 1973), American journalist
# William Dobson (academic)

William Dobson, (30 March 1650 - 15 June 1731) was an English academic.
Dobson was born in Hampshire and educated at Trinity College, Oxford. He was President of Trinity from 1706 until his death. He also held the livings at Cliddesden, Farleigh and Garsington.
# WHYP

WHYP may refer to:
* WHYP-LP, a low-power radio station (98.9 FM) licensed to serve Corry, Pennsylvania, United States
* WWCB, a radio station (1370 AM) licensed to serve Corry, Pennsylvania, which held the call sign WHYP from 2010 to 2013
# William Fortescue, 1st Earl of Clermont

William Henry Fortescue, 1st Earl of Clermont, KP (5 August 1722 – 30 September 1806), was an Irish peer and politician.

## Origins

He was the eldest son of Thomas Fortescue (1683–1769), a Member of Parliament for Dundalk. His younger brother was James Fortescue, MP and Privy Counsellor.

## Career

He served as High Sheriff of Louth in 1746. He represented County Louth in the Irish House of Commons from 1745 to 1760 and subsequently the borough of Monaghan from 1761 to 1770. In 1768 he sat briefly as Member of Parliament for Dundalk before opting to sit for Monaghan Borough, for which he had also been elected. He was appointed Governor and Custos Rotulorum of County Monaghan for life in 1775, standing down just before his death in 1806. He was created Earl of Clermont in 1777 and a Knight Founder of the Order of St Patrick on 30 March 1795. He was a francophile and it is believed on that account he selected Clermont as the name of his earldom.
He had horseracing interests and his racing silks were all crimson. He was known in racing circles as the Father of the Turf and won the Derby with his horse Aimwell. He had a country estate in Norfolk.
His London townhouse was 44 Berkeley Square in Mayfair, which he purchased from George Finch-Hatton in 1774, after the death of its builder, Lady Isabella Finch (1700–1771), the 7th daughter of Daniel Finch, 7th Earl of Winchilsea. In the early 1960s it became the home of the Clermont Club, an exclusive gambling club, and its basement and garden were occupied until 2018 by the then exclusive nightclub Annabel's.

## Marriage and progeny

He married Frances Cairnes Murray, a daughter and co-heiress of Colonel John Murray, MP for County Monaghan, by whom he had an only daughter:
* Louisa Fortescue.

## Death, burial and succession

He died aged 85 at Brighton on 29 September 1806, without male progeny, and was buried at Little Cressingham Church in Norfolk, in which parish was situated Clermont Lodge (now Clermont Hall), his shooting lodge. As he died without male progeny his earldom of Clermont and 1770 barony of Clermont became extinct, whilst his viscountcy and 1776 barony of Clermont were inherited by his nephew William Charles Fortescue, who had been MP for County Louth and then County Louth since 1796.

## Monument in St Andrew's Church, Little Cressingham

A mural monument survives in St Andrew's Church, Little Cressingham, inscribed as follows:
    Near this place lyeth the body of William Henry Fortescue Viscount Clermont, and Earl of Clermont in Ireland, who departed this life on the 29th day of September, 1806, in the 85th year of his age. This monument is erected in obedience to his will by his executor William Charles Fortescue, now Viscount Clermont, who was in Ireland at the time of his decease.
# Aden, Illinois

Aden is an unincorporated community in Hamilton County, Illinois, United States. Aden is 6 miles (9.7 km) west of Mill Shoals.

## History

Aden was originally called Lower Hills. A post office was established at Lower Hills in 1875, and the post office was renamed Aden in 1894.
# Helena, California

Helena is a ghost town in unincorporated Trinity County, California, United States. It is located on the North Fork of the Trinity River, 10 miles (16 km) west-northwest of Weaverville. State Route 299 runs right past the former town to the south; East Fork Road connects the highway to Helena.

## History

The community was settled in 1851 as a mining camp on the site of an old Chimariko village. It was known as Bagdad, North Fork, and The Cove before its post office opened in 1891; the post office was named Helena after the postmaster Mr. Meckel's wife to avoid confusion with another California community called North Fork.
John and Christian Meckel, who moved to the area and established a home on a group of mining claims that totaled 160 acres. In 1854, the Meckels opened a general merchandise store and later a hotel. The town was first known as North Fork, but it was popularly known as “Baghdad,” a name given to the settlement reportedly because it was as rowdy and bizarre as the ancient city with the same name on the Tigris River.
In 1859 the Meckel brothers built and operated a brewery in Helena, then called North Fork.
In 1923, the final stretch of road was built from Helena to South Fork, which connects it to the coast.
When the gold mining dried up, the town soon followed, with slight upticks during the Great Depression. When State Route 299 was completed in 1931, it ended the necessity of the town as it was now being bypassed. The entire town was then bought by F. I. DiNapoli in 1966 for $50,000.
In 1984, Helena was added to the National Register of Historical Places.

## Current status

Today, Helena is abandoned and owned by the trustee of a deceased businessman from San Jose. The Currie Cottage (1859), the Meckel Store (1858), the Shlomer Brick Building (1859), The Shlomer Feed Stable (1860), the Meckel Barn (1860), and a rental building built in the 1930s remain.
# Helena, Guyana

Helena is a village in the Demerara-Mahaica Region of Guyana. Administratively the village is subdivided in Helena No.1 and Helena No.2 and is part of the Mahaica subregion.

## History

Helena started as a sugar plantation. By 1896, the plantation was abandoned and purchased by the government of British Guiana to be divided into small lots. The settlement initially suffered from neglect, because many of the owners did not live in the village. In 1848, construction started on the Demerara-Berbice Railway linking Georgetown with New Amsterdam. In August 1864, the railway reached Helena where the Mahaica station opened. The station remained the terminus until 1890 when work resumed. The railway closed in 1972.

## Overview

The economy of Helena is mainly based on farming. Helena has a primary school, and a private secondary school. The village has one church and two mandirs. In 2008, a statue of Sir James Douglas, the first governor of British Columbia, was unveiled in front of the former railroad station, because he was born and raised in the region.
# Helena's Social Supremacy

Helena's Social Supremacy (1894), also known as Helena's Social Supremacy – Montana's Center of Fashion, Refinement, Gentility, Etiquet, Kettle Drums, High Fives, Progressive Euchre, and Mixed Drinks, is a satirical pamphlet created during the Montana capital referendum by Charles H. Eggleston, the editor of the Anaconda Standard.

## Background

The pamphlet was published during the Montana capital referendum, conducted in two parts in 1892 and 1894. In 1892, several cities entered to become the state capital, but none of them won a majority; a second round was held in 1894 between Helena and Anaconda. Both Helena and Anaconda were problematic cities for voters. Where Helena, as the temporary capital, had been embroiled in political dysfunction—early Montana legislatures were chaotic, with deadlock only addressed through precarious political compromises—Anaconda was perceived as a working-class, industrial city under the control of Marcus Daly and his corporations.

## Publication and contents

The pamphlet was created by Charles H. Eggleston, the editor of the Anaconda Standard, though it lists no author. It masqueraded as a supplement to An Address to the People of Montana, a pro-Helena pamphlet that degraded the city of Anaconda for its working-class, little-educated, and industrial population. Although the pamphlet lists Helena as its original print location, and a contemporaneous newspaper account said the pamphlet was printed "by some every-day citizen of Helena" who was "disgusted" with An Address to the People of Montana, Helena's Social Supremacy was likelier printed elsewhere. It contains 48 pages, some with illustrations, and has a page size of 16.5 × 11.2 cm. Upon its completion, the Great Falls Weekly Tribune reported that the committee in charge of the Address sent an attaché of "paid spies" to uncover the author's identity.
The pamphlet played into the view of Helena as a pretentious and elite city. In one segment, it reported that Helena had hundreds of women—774—who owned poodle dogs, while Anaconda had precisely zero. Where the Address had painted Marcus Daly—the corporate leader of Anaconda—as rapacious, the satire instead developed a rags to riches story of an egalitarian gentleman; the satire said the apparent ineffectiveness of the Address in demonstrating his greed was because of Helena's "proverbial tenderness of heart and nobility of soul". It satirized the Helenan view of other towns by portraying them as relatively advanced and progressive: Boulder boys and girls finely danced, the residents of Phillipsburg brushed their teeth, and Anacondans did not consider it "good fun to interrupt funeral services with a charivari" (mock parade).
Although thousands of copies of the pamphlet were probably produced in the lead-up to the referendum, an estimate in 1940 placed the number surviving at around six. Around that time, one copy was repatriated to Montana—and then to the state treasurer's archives—after being held on the East Coast for several decades.
# William Fraser Hume

Dr. William Fraser Hume FRSE (1867–1949) was a British geologist specialising in Egypt.

## Life

He was born in Cheltenham in England on 1 October 1867 the son of George Hume.
He received his early education in Russia and at College Galliard in Lausanne in Switzerland. He then attended the Royal College of Science and Royal College of Mines in the University of London under John Wesley Judd graduating BSc around 1887. He began lecturing at the Royal College of Science in 1890 and received a doctorate (DSc) in 1893.
In 1897, he moved to Egypt to assist with a huge geological survey of the whole country and in 1909 became Director of the entire Geological Survey of Egypt. In 1910, he was elected a Fellow of the Royal Society of Edinburgh. His proposers were John Horne, Ben Peach, John Walter Gregory, Sir John Smith Flett and James Ireland.
During the First World War he advised on water supply to the British Army in Egypt and the Middle East. He was awarded the Lyell Medal by the Geological Society of London in 1919.
He served as president of the Royal Geographical Society of Egypt from December 1926 to May 1946. and as president of the Institute of Egypt in 1928.
He retired in 1927 and returned to England to Sussex around 1930 and died there on 23 February 1949. He is buried in Littlehampton Cemetery.

## Publications

* Rift Valleys and Geology of the Eastern Sinai (1901)
* The Topography and Geology of the Peninsula of Sinai (1906)
* Report on the Oilfield Region of Egypt (1916)
* Geology of Egypt (1925)
* Phosphate Deposits in Egypt (1927)

## Family

He married Ethel Gladys Williams.