A117105 Numbers that are the sum of three positive heptagonal numbers (A000566) in at least one way.

3, 9, 15, 20, 21, 26, 32, 36, 37, 42, 43, 48, 53, 54, 57, 59, 63, 69, 70, 74, 75, 80, 83, 86, 89, 90, 91, 95, 96, 100, 102, 106, 107, 111, 114, 116, 117, 120, 122, 123, 126, 128, 131, 133, 137, 143, 144, 147, 148, 149, 150, 153, 154, 156, 162, 163, 164, 165

Offset

1,1

Comments

7 is the only prime heptagonal number. Primes which are sums of two positive heptagonal numbers include: {2, 19, 41, 73, 89, 113, 149, 167, 193, 223, 229, 269, 293, 337, 347, 367, 383, ...}. Primes which are sums of three positive heptagonal numbers include: {3, 37, 43, 53, 59, 83, 89, 107, 131, 137, 149, 163, 167, 173, 191, 197, 211, 227, 241, 251, 257, 263, 271, ...}.

By definition this does not contain any repeated terms. - N. J. A. Sloane, Aug 15 2020

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

{a(n)} = {A000566} + {A000566} + {A000566} = {a*(5*a-3)/2 + b*(5*b-3)/2 + c*(5*c-3)/2} \ {A000566}.

Mathematica

With[{nn=10}, Select[Union[Total/@Tuples[PolygonalNumber[7, Range[ nn]], 3]], #<=PolygonalNumber[7, nn]-2&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 16 2020 *)

Crossrefs

Cf. A000566, A000040, A000326, A003679, A064826, A117065.

Sequence in context: A071347 A093414 A123998 * A261190 A282031 A307202

Adjacent sequences: A117102 A117103 A117104 * A117106 A117107 A117108

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 18 2006

Extensions

Missing 106 and 131 added by Giovanni Resta, Jun 15 2016

Corrected (deleting duplicates) and extended by Harvey P. Dale, Aug 16 2020

Status

approved