A065999 Sum of digits of 9^n.

1, 9, 9, 18, 18, 27, 18, 45, 27, 45, 45, 45, 54, 63, 72, 63, 63, 99, 81, 90, 90, 90, 90, 108, 117, 144, 117, 108, 90, 126, 99, 153, 144, 117, 153, 144, 162, 171, 153, 153, 153, 198, 162, 171, 198, 216, 171, 198, 198, 225, 153, 252, 216, 234, 207

Offset: 0

Author

N. J. A. Sloane, Dec 11 2001

Keywords

• nonn
• easy
• base

Comments

a(n) mod 9 = 0 for n > 0. - Reinhard Zumkeller, May 14 2011

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• M. Sapir et al., The Decimal Expansions of Powers of 9: Problem 10758, Amer. Math. Monthly, 108 (Dec., 2001), 977-978.
• H. G. Senge and E. G. Straus, PV-numbers and sets of multiplicity, Periodica Math. Hungar., 3 (1971), 93-100.
• C. L. Stewart, On the representation of an integer in two different bases, J. Reine Angew. Math., 319 (1980), 63-72.

Crossrefs

Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), A065713 (k=4), A066001 (k=5), A066002 (k=6), A066003(k=7), A066004 (k=8), this sequence (k=9), A066005 (k=11), A066006 (k=12), A175527 (k=13).

Cf. also A056888, A001019.

Programs

Mathematica

Table[Total[IntegerDigits[9^n]], {n, 0, 60}] (* Vincenzo Librandi, Oct 08 2013 *)

PARI

a(n) = sumdigits(9^n); \\ Michel Marcus, Nov 01 2013

Formula

a(n) = A007953(A001019(n)). - Michel Marcus, Nov 01 2013