| --- |
| license: cc0-1.0 |
| pretty_name: "Integer Sequences" |
| tags: |
| - mathematics |
| - integers |
| - sequences |
| - primes |
| - combinatorics |
| - number-theory |
| --- |
| |
| # Integer Sequences |
|
|
| Many integer sequences as one-value-per-line CSV files. |
| Generated from formulas, recurrences, sieves, and filters. |
| Primes sourced from https://t5k.org. |
|
|
| ## Contents |
|
|
| Each file in `base/` holds one sequence, one integer per line, |
| sorted ascending. |
|
|
| ### Figurate and geometric |
|
|
| - `triangular`, `pentagonal`, `hexagonal`, `heptagonal`, `star` |
| - `pow-2`, `pow-3`, `pow-5`, `pow-7` |
| - `tetrahedral`, `pentatope`, `octahedral` |
| - `square-pyramidal`, `stella-octangula` |
| - `icosahedral`, `dodecahedral`, `rhombic-dodecahedral` |
| - `truncated-tetrahedral`, `truncated-octahedral`, `truncated-cube` |
| - `centered-triangular`, `centered-square`, `centered-pentagonal`, |
| `centered-hexagonal`, `centered-heptagonal`, `centered-octagonal`, |
| `centered-decagonal` |
| - `N-gonal-pyramidal` (3 through 20) |
| - `N-centered-polygonal` (3 through 11) |
| - `pronic` |
|
|
| ### Recurrence-based |
|
|
| - `fibonacci`, `lucas`, `padovan`, `tribonacci`, `pell`, `jacobsthal` |
| - `catalan`, `bell`, `motzkin`, `delannoy`, `derangement` |
| - `partition`, `planar-partitions` |
| - `euler-number`, `stirling-second` |
| - `look-and-say`, `sylvester`, `recaman`, `stern-brocot` |
|
|
| ### Prime and factoring |
|
|
| - `prime` (50 million, from t5k.org) |
| - `twin-prime`, `safe-prime`, `sophie-germain-prime`, `super-prime` |
| - `semiprime`, `sphenic`, `composite` |
| - `square-free`, `powerful` |
| - `primorial` |
|
|
| ### Digit and filter |
|
|
| - `palindromic`, `happy`, `harshad`, `abundant`, `deficient` |
| - `binary-even` (evil numbers), `smith`, `lucky` |
| - `undulating`, `narcissistic`, `automorphic`, `kaprekar` |
| - `collatz-length`, `euler-totient`, `divisors` |
|
|
| ### Other |
|
|
| - `natural`, `n-eq-3-mod-4`, `factorial`, `repunit` |
| - `binary-base-tree` (Wedderburn-Etherington) |
| - `highly-composite`, `amicable` |
| - Static lookups: `perfect`, `weird`, `order-of-simple-groups`, |
| `connected-planar-graph`, `number-of-connected-graphs`, |
| `planar-graph`, `irreducible-polynomials` |
|
|
| ## Sources |
|
|
| - **The Prime Pages (t5k.org)**: https://t5k.org/lists/small/millions/ |
| - **OEIS**: https://oeis.org (reference for sequence definitions) |
|
|
| ## License |
|
|
| CC0-1.0. The sequences are mathematical facts, not creative works. |
|
|
