login
A117105
Numbers that are the sum of three positive heptagonal numbers (A000566) in at least one way.
2
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
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
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