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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.
Contents
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 (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 (first 4 sexagesimal digits) |
c. 700 bc | Baudhayana, Shulba Sutras | A001333/A000129 | Calculations of (8th convergent) |
c. 475 bc | Traditionally, Hippasus of Metapontum | A002193 | Irrationality of |
c. 450 bc | Anaxagoras of Clazomenae | A002161 | Squaring the circle |
c. 370 bc | Theaetetus of Athens | A000037 | Irrationality of 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. 100 bc | Antikythera mechanism | A240136 | Prime numbers of uncertain meaning |
c. 60 | Heron (or Hero) of Alexandria, Metrica | A010670 | Calculation of |
c. 100 | Nicomachus | A000537 | Sum of the first 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 ) |
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 |
c. 1180 | Arnaut Daniel's sestinas | A239132 | 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 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 |
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 |
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 |
1744 | Leonhard Euler | A096444 | 'Fourier series' for |
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.
Notes
Cite this page as
Charles R Greathouse IV, Alonso del Arte, and Antti Karttunen, Historical sequences.— From the On-Line Encyclopedia of Integer Sequences® Wiki (OEIS® Wiki). [https://oeis.org/wiki/Historical_sequences]