%I #35 Sep 07 2024 15:39:39

%S 1,9,9,18,18,27,18,45,27,45,45,45,54,63,72,63,63,99,81,90,90,90,90,

%T 108,117,144,117,108,90,126,99,153,144,117,153,144,162,171,153,153,

%U 153,198,162,171,198,216,171,198,198,225,153,252,216,234,207

%N Sum of digits of 9^n.

%C a(n) mod 9 = 0 for n > 0. - _Reinhard Zumkeller_, May 14 2011

%H N. J. A. Sloane, <a href="/A065999/b065999.txt">Table of n, a(n) for n = 0..10000</a>

%H M. Sapir et al., <a href="https://www.jstor.org/stable/2695428">The Decimal Expansions of Powers of 9: Problem 10758</a>, Amer. Math. Monthly, 108 (Dec., 2001), 977-978.

%H H. G. Senge and E. G. Straus, <a href="https://doi.org/10.1007/BF02018464">PV-numbers and sets of multiplicity</a>, Periodica Math. Hungar., 3 (1971), 93-100.

%H C. L. Stewart, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002197707">On the representation of an integer in two different bases</a>, J. Reine Angew. Math., 319 (1980), 63-72.

%F a(n) = A007953(A001019(n)). - _Michel Marcus_, Nov 01 2013

%t Table[Total[IntegerDigits[9^n]], {n, 0, 60}] (* _Vincenzo Librandi_, Oct 08 2013 *)

%o (PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }

%o { for (n=0, 1000, a=SumD(9^n); write("b065999.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 06 2009

%o (PARI) a(n) = sumdigits(9^n); \\ _Michel Marcus_, Nov 01 2013

%Y 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).

%Y Cf. also A056888, A001019.

%K nonn,easy,base

%O 0,2

%A _N. J. A. Sloane_, Dec 11 2001