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%I #19 Jan 29 2020 04:40:59
%S 2,1,31,62,11,174,120,1352,1168,1140,2602,1244,1394,2287,2982,4469,
%T 644,3073,1879,10771,1309,17437,35739,734,17425,30566,27350,45142,
%U 33266,37592,32212,56555,20376,29832,66403,111466,116150,98808,15668,14279,63561
%N Consider all integer triples (i,j,k), j,k>0, with i^3=j^3+binomial(k+2,3), ordered by increasing i; sequence gives j values.
%C i values are A054234 and k values are A054236
%H Jon E. Schoenfield, <a href="/A054235/b054235.txt">Table of n, a(n) for n=1..41</a>
%e 4^3 = 64 = 2^3+binomial(6+2,3); 11^3 = 1331 = 1^3+binomial(19+2,3).
%t (* This is just a re-computation of A054235, given A054234 *)
%t A054234 = Cases[Import["https://oeis.org/A054234/b054234.txt", "Table"], {_, _}][[All, 2]];
%t A054235 = Reap[ Do[ Do[ r = Reduce[ i^3 == j^3 + Binomial[k+2, 3], k, Integers]; If[r =!= False, ijk = {i, j, k} /. ToRules[r]; Print[ijk]; Sow[ijk[[2]]]; Break[]], {j, 1, i-2}], {i, A054234}]][[2, 1]] (* _Jean-François Alcover_, Jan 03 2013, updated Jan 24 2020 *)
%K nice,nonn
%O 1,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 07 2000
%E More terms from _Jon E. Schoenfield_, Jan 19 2009
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