A117105 - OEIS

%I #12 Aug 16 2020 11:21:56

%S 3,9,15,20,21,26,32,36,37,42,43,48,53,54,57,59,63,69,70,74,75,80,83,

%T 86,89,90,91,95,96,100,102,106,107,111,114,116,117,120,122,123,126,

%U 128,131,133,137,143,144,147,148,149,150,153,154,156,162,163,164,165

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

%C 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, ...}.

%C By definition this does not contain any repeated terms. - _N. J. A. Sloane_, Aug 15 2020

%H Harvey P. Dale, <a href="/A117105/b117105.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 *)

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

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 18 2006

%E Missing 106 and 131 added by _Giovanni Resta_, Jun 15 2016

%E Corrected (deleting duplicates) and extended by _Harvey P. Dale_, Aug 16 2020