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

Author

Joan Llobera Querol, Sep 22 2023

Keywords

• nonn

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.

Examples

			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).
		

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.

Crossrefs

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

Programs

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