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%I #21 Jan 29 2020 04:41:06
%S 6,19,132,182,217,757,2377,2077,2833,4374,2408,4864,4912,6097,7295,
%T 3324,8341,13357,17522,20006,25939,20406,24492,68984,75732,69151,
%U 79000,69361,97598,99064,126014,126873,154622,174278,180514,136431,117151,198310,238630,282961,297815
%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 k values.
%C i values are A054234 and j values are A054235.
%H Jon E. Schoenfield, <a href="/A054236/b054236.txt">Table of n, a(n) for n=1..41</a>
%e 4^3 = 64 = 2^3 + binomial(6+2,3);
%e 11^3 = 1331 = 1^3 + binomial(19+2,3).
%t (* This is just a re-computation of A054236, given A054234 *)
%t A054234 = Cases[Import["https://oeis.org/A054234/b054234.txt", "Table"], {_, _}][[All, 2]];
%t A054236 = 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[[3]]]; Break[]], {j, 1, i-2}], {i, A054234}]][[2, 1]] (* _Jean-François Alcover_, Jan 2013, updated Jan 24 2020 *)
%Y Cf. A054234, A054235.
%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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