A133251 Heptagonal numbers A000566 which are the sum of two other heptagonal numbers > 0.

697, 3186, 3744, 5221, 7209, 8323, 12496, 12852, 19228, 20566, 21022, 24850, 29539, 35224, 38254, 40768, 44023, 44689, 52345, 53802, 58293, 62173, 63760, 66178, 67815, 78057, 79834, 80730, 82537, 95746, 97713, 101707, 115240, 131905, 135373

Offset

1,1

Comments

This is to A000566 as A136117 is to A000326.

The sequence contains 12852 and 19751431167846, which are the smallest heptagonal numbers equal to twice another heptagonal number. - R. J. Mathar, Jan 13 2008

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Heptagonal Number.

Formula

{x such that x in A000566 and x = A000566(i) + A000566(j) for i, j > 0 and where A000566(k) = k*(5*k-3)/2}.

Example

Where hep(k) = k-th heptagonal number = A000566(k):
a(1) = 697 = hep(17) = 616 + 81 = hep(16) + hep(6).
a(2) = 3186 = hep(36) = 1782 + 1404 = hep(27) + hep(24).
a(3) = 3744 = hep(39) = 2673 + 1071 = hep(33) + hep(21).
a(4) = 5221 = hep(46) = 4347 + 874 = hep(42) + hep(19).

Mathematica

Module[{nn=1000, heps}, heps=Table[(n(5n-3))/2, {n, nn}]; Select[ Union[ Total/@ Tuples[Take[heps, nn/2], 2]], MemberQ[heps, #]&]] (* Harvey P. Dale, Dec 18 2015 *)

Crossrefs

Cf. A000566, A136117.

Sequence in context: A185377 A118059 A028500 * A243837 A116338 A293203

Adjacent sequences: A133248 A133249 A133250 * A133252 A133253 A133254

Keyword

nonn

Author

Jonathan Vos Post, Dec 19 2007

Extensions

More terms from R. J. Mathar, Jan 13 2008

Status

approved