login
A365905
"2-peloton numbers": Numbers that appear at least twice in A365904.
1
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
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
KEYWORD
nonn
AUTHOR
Joan Llobera Querol, Sep 22 2023
STATUS
approved