A054205 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 i values.

5, 95, 216, 566, 728, 804, 1625, 2044, 9393, 11387, 13503, 14014, 19520, 22874, 27545, 34182, 38368, 39388, 39878, 50953, 69977, 76200, 98494, 107976, 141750, 143424, 230094, 251263, 466655, 521016, 572886, 616712, 724625, 1211267, 1346927, 1383317, 1810998, 1883791, 1985794, 1999374, 2015494, 2066496, 2174526

Offset

1,1

Comments

The tetrahedral number A000292(a(n)-1) is the sum of two positive cubes. The j values are in A054206 and k values in A054207.

A sum of two cubes can only have 25 distinct values (mod 63). In a search, this means only 75 values for i (mod 189) need to be evaluated. - Bert Dobbelaere, Jan 13 2019

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..53

Example

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

Mathematica

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}]; First /@ lst (* Robert G. Wilson v, Jan 15 2007 *)

Crossrefs

Cf. A054206, A054207, A000292.

Sequence in context: A195854 A153227 A116159 * A116290 A274874 A275292

Adjacent sequences: A054202 A054203 A054204 * A054206 A054207 A054208

Keyword

nice,nonn

Author

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

Extensions

More terms from Martin Fuller, Nov 27 2006

Terms a(30)-a(36) from Jon E. Schoenfield, Jan 14 2009

Offset corrected by N. J. A. Sloane, Jan 14 2009

Terms a(37)-a(43) from Jon E. Schoenfield, Aug 30 2013

Status

approved