A117104 Sum of two positive heptagonal numbers A000566.

2, 8, 14, 19, 25, 35, 36, 41, 52, 56, 62, 68, 73, 82, 88, 89, 99, 110, 113, 115, 119, 130, 136, 146, 149, 155, 162, 166, 167, 182, 190, 193, 196, 203, 207, 223, 224, 229, 236, 242, 244, 253, 260, 269, 270, 287, 290, 293, 296, 301, 304, 316, 320, 337, 341, 343, 347

Offset: 1

Author

Jonathan Vos Post, Apr 18 2006

Keywords

• easy
• nonn

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, ...}.

Crossrefs

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

Programs

Mathematica

Lim=348;nl=Ceiling[Sqrt[(2/5)Lim]];Select[Union[Total/@Tuples[Table[n*(5n-3)/2,{n,nl}],{2}]],#James C. McMahon, Sep 27 2024 *)

Formula

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

Extensions

Missing 343 added by Giovanni Resta, Jun 15 2016