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A054206 Consider all integer triples (i,j,k), j >= k > 0, with binomial(i+2,3)=j^3+k^3, ordered by increasing i; sequence gives j values. 3

%I

%S 3,49,106,306,348,443,830,1103,5169,6135,6427,7512,10668,12465,14061,

%T 18456,20463,17943,21919,27766,38509,41932,53284,54040,67330,78418,

%U 102298,135082,238207,286706,279850,319935,373785,665863,734790,759731,995600,987492,998289,1100210,963913,1119792,1196684

%N Consider all integer triples (i,j,k), j >= k > 0, with binomial(i+2,3)=j^3+k^3, ordered by increasing i; sequence gives j values.

%C The i values are in A054205 and k values in A054207.

%H Bert Dobbelaere, <a href="/A054206/b054206.txt">Table of n, a(n) for n = 1..53</a>

%e binomial(5+2,3)=35=2^3+3^3; binomial(95+2,3)=147440=49^3+31^3;

%t lst = {}; Do[ b = Binomial[i + 2, 3]; j = Floor[b^(1/3)]; lmt = Ceiling[j/2]; While[ k = (b - j^3)^(1/3); j > lmt && !IntegerQ[k], j-- ]; If[j != lmt, Print[{i, j, k}]; AppendTo[lst, {i, j, k}]], {i, 2, 30000}]; (Transpose@lst)[[2]] (* _Robert G. Wilson v_, Jan 15 2007 *)

%Y Cf. A054205, A054207, A000292.

%K nice,nonn

%O 1,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 28 2000

%E More terms from _Martin Fuller_, Nov 27 2006

%E Offset corrected by _N. J. A. Sloane_, Jan 14 2009

%E a(30)-a(36) from _Jon E. Schoenfield_, Jan 14 2009

%E a(37)-a(43) from _Jon E. Schoenfield_, Aug 30 2013

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)