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
Keywords
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.
Programs
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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
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