cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A274578 Nonsquare k such that k^3 - 1 is the average of two positive cubes.

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%I A274578 #38 Jul 27 2025 11:36:05
%S A274578 2305,2629,4117,7060,37444,46081,113320,208545,449569,474553,507325,
%T A274578 1224757,1499068,1927405,1931077,2263129,2350909,2447596,3107841,
%U A274578 4065517,4274932,4303321,5646685,6582865,7225597,10386273,18432001,21936709,24218425,24362989,27351417
%N A274578 Nonsquare k such that k^3 - 1 is the average of two positive cubes.
%C A274578 The equation x^3 + y^3 = 2*z^3 has no integer solution triple (x, y, z) for x > y and z is nonzero. So this sequence focuses on the equation x^3 + y^3 = 2*(z^3 - 1) where x, y > 0.
%H A274578 Chai Wah Wu, <a href="/A274578/b274578.txt">Table of n, a(n) for n = 1..66</a>
%e A274578 2305 is a term because it is not a square and 2305^3 - 1 = (144^3 + 2904^3) / 2.
%o A274578 (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
%o A274578 lista(nn) = for(n=1, nn, if(isA003325(2*(n^3-1)) && !issquare(n), print1(n, ", ")));
%Y A274578 Cf. A000037, A003325, A068601, A273822.
%K A274578 nonn
%O A274578 1,1
%A A274578 _Altug Alkan_, Jun 29 2016
%E A274578 a(9)-a(25) from _Chai Wah Wu_, Aug 07 2020
%E A274578 a(26)-a(31) from _Chai Wah Wu_, Jun 30 2025