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# Historical sequences

This is a project for finding historical sequences, locating early references, and for antedating existing sequences. Finding early works and their translations, and making them available on the OEIS, is also included.

The primary focus is on sequences or constants referenced explicitly, though sometimes implicit references to sequences are useful as well.

## Examples

The main interest is in finding less-well-known references, but this table covers many well-known sequences. Of course even these sequences often lack references to their antiquity; please add information where available!

Year Reference Sequences Notes
c. 33,000 bc Lebombo bone A000027 29 tally marks
c. 20,000 bc Ishango bone A100000 Markings of unknown meaning
c. 2600 bc VAT 12593 A000290 A table of lengths and the associated areas of squares
c. 2500 bc BM 92698 A000578 A table of numbers and their cubes
c. 1900 bc Copy preserved in the Rhind Papyrus A000796, A094871 Calculations of ${\displaystyle \pi }$ (2 decimal digits equivalent)
c. 1800 bc Plimpton 322 A009000, A046083 Pythagorean triples
c. 1800 bc M 08613 A000079 Powers of 2
c. 1700 bc YBC 7289 A070197 Calculations of ${\displaystyle \scriptstyle {\sqrt {2}}}$ (first 4 sexagesimal digits)
c. 700 bc Baudhayana, Shulba Sutras A001333/A000129 Calculations of ${\displaystyle \scriptstyle {\sqrt {2}}}$ (8th convergent)
c. 475 bc Traditionally, Hippasus of Metapontum A002193 Irrationality of ${\displaystyle \scriptstyle {\sqrt {2}}}$
c. 450 bc Anaxagoras of Clazomenae A002161 Squaring the circle
c. 370 bc Theaetetus of Athens A000037 Irrationality of ${\displaystyle \scriptstyle {\sqrt {n}}}$ for nonsquare n
c. 370 bc Theaetetus of Athens A053016 Platonic solids
c. 350 bc Thymaridas of Paros A000040 Prime numbers
c. 300 bc Euclid, Elements A000396, A000668 Perfect numbers and Mersenne primes
c. 250 bc Archimedes of Syracuse A092537 Archimedian solids
c. 173 bc Divination Pan of the Supreme Unity moving around Nine Palaces (太一行九宮占盤) A033812 Luo Shu Square
c. 150 bc Hypsicles of Alexandria (credited by Diophantus) A000217, A000290, etc. Polygonal numbers
c. 60 Heron (or Hero) of Alexandria, Metrica A010670 Calculation of ${\displaystyle \scriptstyle {\sqrt[{3}]{100}}}$
c. 100 Nicomachus A000537 Sum of the first ${\displaystyle n}$ cubes
c. 100 Nicomachus' Introduction to Arithmetic A000396, A005100, A005101 Perfect, deficient, and abundant numbers
c. 220 Hippolytus' Refutation of All Heresies A010888 Digital roots
c. 300 Sefer Yetzirah, Chapter IV A000142 Factorials
c. 700 Virahanka A000045 Fibonacci numbers
c. 800 Alcuin, Propositiones ad Acuendos Iuuenes A005044 Number of triangles with integer sides and perimeter n
954 inscription on the Parsvanatha Temple, Khajuraho A126710 Most-perfect magic square
c. 975 Halayudha's Mṛtasañjīvanī (commentary on the Chandaḥśāstra) A007318 Pascal's triangle
1202 Leonardo of Pisa (Fibonacci), Liber Abaci A000045 Popularization of (among others) the Fibonacci numbers
c. 1300 Zhu Shijie's Siyuan yujian A000292, A000332, etc. Formulas for sums of polynomials
1322 Levi ben Gershon (Gersonides), The Harmony of Numbers A003586 3-smooth numbers
1356 Narayana Pandit, Ganita Kaumudi A010467 Calculation of ${\displaystyle \scriptstyle {\sqrt {10}}}$ and other roots
14th c? Narayana Pandit A000930 Narayana's cows
1410 Jan Šindel and Mikuláš of Kadaň, Orloj A028354, A028355 Sequence of astronomical clock chimes
1557 Robert Recorde, The Whetstone of Witte A201186 One of many incorrect lists of perfect numbers
1619 Johannes Kepler, Harmonices Mundi, Liber III, Caput II, Linz A093873/A093875 Kepler's tree of harmonic fractions.
1638 Galileo Galilei, Two New Sciences A000290 Paradox of infinity
1644 Marin Mersenne, Cogitata Physica-Mathematica A109461 Attempt to enumerate exponents for the Mersenne primes
1685 Adam Kochański, Observationes Cyclometricae... A199657/A199658 Calculations of ${\displaystyle \pi }$
1693 Bernard Frénicle de Bessy, Des carrez ou tables magiques A006052 Number of magic squares
1699 Sébastien Le Prestre de Vauban A224749 Vauban's sequence
c. 1730 Minggatu A000108 Catalan numbers
1735 Leonhard Euler, De summis serierum reciprocarum A132049/A132050 Formula for computing ${\displaystyle \pi }$
1744 Leonhard Euler A096444 'Fourier series' for ${\displaystyle \scriptstyle (\pi -1)/2.}$
c. 1750 Benjamin Franklin A124472 Magic square of order 16
1774 Lagrange, Additions aux éléments d'algèbre... A001175 Pisano periods
1778 Leonhard Euler, Facillima methodus... A000926 Numeri idonei

## Ideas for new sequences

• Quipu are known to record sequences of natural numbers. Are any particular examples notable enough for inclusion? Presumably most contained non-mathematical information, but then again A100000 presumably did as well.

## Antedating sequences

Finding earlier references to existing sequences is always useful, even if the sequence is not actually historical.

## Finding references

Original sources can be hard to come by. Some old books (or reprints) can be found on Google Books or the arXiv: see for example Euler on the arXiv. JSTOR and other archiving services have some articles back to the 16th century.

• Costantino Sigismondi, Gerbert of Aurillac: astronomy and geometry in tenth century Europe, arXiv:1201.6094.
• I was not able to find any integer sequences in Suàn shù shū (Writings on Reckoning)