A365905 "2-peloton numbers": Numbers that appear at least twice in A365904.

15, 36, 43, 49, 64, 66, 78, 85, 99, 100, 118, 120, 134, 141, 151, 159, 168, 169, 190, 204, 210, 211, 219, 225, 241, 246, 253, 256, 270, 274, 279, 283, 288, 295, 309, 321, 323, 325, 345, 351, 355, 358, 364, 372, 376, 379, 386, 393, 394, 400, 405, 406, 423, 429, 435, 438, 440, 456, 463, 474, 484, 498

Offset

1,1

Comments

Called "peloton" numbers after the original sequence idea in first link: the difference of a rhombus (a square number) and a triangular number, placed as points on a triangular grid, form the shape of a peloton in bicycle racing.

Contains all elements of A001110 other than 0 and 1.

Links

Eric Snyder, Table of n, a(n) for n = 1..10000

Zach Wissner-Gross, Can You Shape the Peloton?, Fiddler on the Proof, Sep 22, 2023.

Example

15 can be obtained as T(4,1) or T(5,4) following notation in A365904.
36 can be obtained as T(6,0) or T(8,7).

Prog

(PARI) isok(n) = sum(m=sqrtint(n), (sqrtint(8*n+1)-1)\2, ispolygonal(m^2-n, 3)) > 1 \\ Andrew Howroyd, Sep 24 2023
(Python/SageMath)
nmax, m, Out = 300, 2, []
Z = [ n^2 - (k^2 + k)/2 for n in [2..nmax] for k in [0..n-1] ]
for i in Z:
    if Z.count(i) >= m: Out.append(i)
Out=sorted(list(set(Out)))
for j in [1..10000]: print(j+1, Out[j])
\\ Eric Snyder, Sep 29 2023

Crossrefs

Cf. A175035 (numbers appear at least once), A365904.

Sequence in context: A241282 A249056 A219096 * A134509 A062712 A224719

Adjacent sequences: A365902 A365903 A365904 * A365906 A365907 A365908

Keyword

nonn

Author

Joan Llobera Querol, Sep 22 2023

Status

approved