A054234 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 i values.

4, 11, 75, 108, 120, 427, 1309, 1583, 1753, 2490, 2712, 2764, 2822, 3678, 4502, 4569, 4595, 7526, 9667, 13723, 14279, 18869, 36367, 37964, 42669, 43738, 46820, 52849, 57666, 59922, 71592, 80480, 85480, 96862, 108383, 121828, 122426, 131318, 131398, 155760, 167021

Offset

1,1

Comments

j values are A054235 and k values are A054236

Links

Jon E. Schoenfield, Table of n, a(n) for n=1..41

Example

4^3=64=2^3+binomial(6+2,3); 11^3=1331=1^3+binomial(19+2,3)

Mathematica

nmax = 21;
ijk[0] = {1, 1, 0};
ijk[n_] := ijk[n] = Module[{i, j, k, r}, For[i = ijk[n-1][[1]]+1, True, i++, r = Reduce[0<j<i && k>0 && i^3 == j^3 + Binomial[k+2, 3], {j, k}, Integers]; If[r =!= False, Return[{i, j, k} /. ToRules[r]]]]];
triples = Reap[For[n=1, n<=nmax, n++, Print[ijk[n]]; Sow[ijk[n]]]][[2, 1]];
triples[[All, 1]] (* Jean-François Alcover, Jan 29 2020 *)

Crossrefs

Sequence in context: A274960 A151826 A032110 * A213328 A181275 A000850

Adjacent sequences: A054231 A054232 A054233 * A054235 A054236 A054237

Keyword

nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 07 2000

Extensions

More terms from Jon E. Schoenfield, Jan 19 2009

Status

approved