A117051 Enneagonal numbers whose sum of digits is also enneagonal.

0, 1, 9, 261, 969, 1350, 6666, 7944, 10071, 13299, 17466, 24486, 33369, 36159, 39804, 42846, 46806, 54375, 57921, 66309, 75264, 80484, 111696, 116754, 128544, 135339, 153825, 167316, 175056, 181374, 204369, 226950, 235950, 243276, 252591, 260169

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

1350 is in the sequence because (1) it is an enneagonal number and (2) the sum of its digits 1+3+5+0=9 is also an enneagonal number

Maple

enne:= proc(x) issqr(56*x+25) and sqrt(56*x+25) mod 7 = 2 end proc:
enne(0):= true:
select(t -> enne(convert(convert(t, base, 10), `+`)), [seq(n*(7*n-5)/2, n=0..1000)]); # Robert Israel, Sep 20 2023

Mathematica

Join[{0}, Select[Table[(n(7n-5))/2, {n, 300}], IntegerQ[(5+Sqrt[25+ 56*Total[ IntegerDigits[#]]])/14]&]] (* Harvey P. Dale, Apr 28 2016 *)

Prog

(PARI) isok(n) = ispolygonal(n, 9) && ispolygonal(sumdigits(n), 9); \\ Michel Marcus, Feb 26 2014

Crossrefs

Cf. A001106.

Sequence in context: A001823 A229259 A117796 * A173985 A280178 A189643

Adjacent sequences: A117048 A117049 A117050 * A117052 A117053 A117054

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Status

approved