Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #26 Oct 23 2023 01:40:01
%S 15,36,43,49,64,66,78,85,99,100,118,120,134,141,151,159,168,169,190,
%T 204,210,211,219,225,241,246,253,256,270,274,279,283,288,295,309,321,
%U 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
%N "2-peloton numbers": Numbers that appear at least twice in A365904.
%C 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.
%C Contains all elements of A001110 other than 0 and 1.
%H Eric Snyder, <a href="/A365905/b365905.txt">Table of n, a(n) for n = 1..10000</a>
%H Zach Wissner-Gross, <a href="https://thefiddler.substack.com/p/can-you-shape-the-peloton">Can You Shape the Peloton?</a>, Fiddler on the Proof, Sep 22, 2023.
%e 15 can be obtained as T(4,1) or T(5,4) following notation in A365904.
%e 36 can be obtained as T(6,0) or T(8,7).
%o (PARI) isok(n) = sum(m=sqrtint(n), (sqrtint(8*n+1)-1)\2, ispolygonal(m^2-n,3)) > 1 \\ _Andrew Howroyd_, Sep 24 2023
%o (Python/SageMath)
%o nmax, m, Out = 300, 2, []
%o Z = [ n^2 - (k^2 + k)/2 for n in [2..nmax] for k in [0..n-1] ]
%o for i in Z:
%o if Z.count(i) >= m: Out.append(i)
%o Out=sorted(list(set(Out)))
%o for j in [1..10000]: print(j+1, Out[j])
%o \\ _Eric Snyder_, Sep 29 2023
%Y Cf. A175035 (numbers appear at least once), A365904.
%K nonn
%O 1,1
%A _Joan Llobera Querol_, Sep 22 2023