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 $\pi$ (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 $\scriptstyle {\sqrt {2}}$ (first 4 sexagesimal digits)
c. 700 bc	Baudhayana, Shulba Sutras	A001333/A000129	Calculations of $\scriptstyle {\sqrt {2}}$ (8th convergent)
c. 475 bc	Traditionally, Hippasus of Metapontum	A002193	Irrationality of $\scriptstyle {\sqrt {2}}$
c. 450 bc	Anaxagoras of Clazomenae	A002161	Squaring the circle
c. 370 bc	Theaetetus of Athens	A000037	Irrationality of $\scriptstyle {\sqrt {n}}$ for nonsquare n
c. 370 bc	Theaetetus of Athens	A053016	Platonic solids
c. 350 bc	Thymaridas of Paros	A000040	Prime numbers
c. 350 bc	Pandrosion of Alexandria	A002580	Doubling the cube (approximation)
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. 120 bc	Hipparchus	A001003	Schröder–Hipparchus numbers
c. 100 bc	Antikythera mechanism	A240136	Prime numbers of uncertain meaning
c. 60	Heron (or Hero) of Alexandria, Metrica	A010670	Calculation of $\scriptstyle {\sqrt[{3}]{100}}$
c. 100	Nicomachus	A000537	Sum of the first $n$ cubes
c. 100	Nicomachus' Introduction to Arithmetic	A000396, A005100, A005101	Perfect, deficient, and abundant numbers
c. 100	Theon's On Mathematics Useful for the Understanding of Plato	A001333, A000129	'Side and diameter numbers' (convergents to $\scriptstyle {\sqrt {2}}$)
c. 220	Hippolytus' Refutation of All Heresies	A010888	Digital roots
c. 300	Sefer Yetzirah, Chapter IV	A000142	Factorials
629	Bhāskara I	A350219	Approximation to sin(1)
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
c. 1180	Arnaut Daniel's sestinas	A239132, A054639	repetitive word order in sestinas
1202	Leonardo of Pisa (Fibonacci), Liber Abaci	A000045	Popularization of (among others) the Fibonacci numbers
1303	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, Gaṇita Kaumudī	A010467	Calculation of $\scriptstyle {\sqrt {10}}$ 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
1424	Jamshīd al-Kāshī The Key to Arithmetic	A125628	Sexagesimal expansion of $2\pi$
1429	Jamshīd al-Kāshī The Treatise of Chord and Sine	A280188	Sexagesimal expansion of sine of 1 degree
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 Cyclometricæ...	A199657/A199658	Calculations of $\pi$
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 $\pi$
1744	Leonhard Euler	A096444	'Fourier series' for $\scriptstyle (\pi -1)/2.$
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. Wampum seemed to fill a similar purpose, though it seems less likely that there are examples with numerical data.

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)
• Many polynomial sequences appear in Ismaël Bullialdus's opus novum ad arithmeticam infinitorum which calculate sums of powers, with great effort, before the Bernoulli numbers or Faulhaber's formula were discovered.

Cite this page as

Charles R Greathouse IV, Alonso del Arte, and Antti Karttunen, Historical_sequences. — From the On-Line Encyclopedia of Integer Sequences® (OEIS®) wiki.Available at https://oeis.org/wiki/Historical_sequences