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

%I A365905 #26 Oct 23 2023 01:40:01
%S A365905 15,36,43,49,64,66,78,85,99,100,118,120,134,141,151,159,168,169,190,
%T A365905 204,210,211,219,225,241,246,253,256,270,274,279,283,288,295,309,321,
%U A365905 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 A365905 "2-peloton numbers": Numbers that appear at least twice in A365904.
%C A365905 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 A365905 Contains all elements of A001110 other than 0 and 1.
%H A365905 Eric Snyder, <a href="/A365905/b365905.txt">Table of n, a(n) for n = 1..10000</a>
%H A365905 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 A365905 15 can be obtained as T(4,1) or T(5,4) following notation in A365904.
%e A365905 36 can be obtained as T(6,0) or T(8,7).
%o A365905 (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 A365905 (Python/SageMath)
%o A365905 nmax, m, Out = 300, 2, []
%o A365905 Z = [ n^2 - (k^2 + k)/2 for n in [2..nmax] for k in [0..n-1] ]
%o A365905 for i in Z:
%o A365905     if Z.count(i) >= m: Out.append(i)
%o A365905 Out=sorted(list(set(Out)))
%o A365905 for j in [1..10000]: print(j+1, Out[j])
%o A365905 \\ _Eric Snyder_, Sep 29 2023
%Y A365905 Cf. A175035 (numbers appear at least once), A365904.
%K A365905 nonn
%O A365905 1,1
%A A365905 _Joan Llobera Querol_, Sep 22 2023