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%I #24 May 18 2017 20:37:44
%S 1,5,7,8,13,11,19,23,25,26,40,38,28,23,34,44,58,56,64,59,61,62,67,74,
%T 82,77,79,89,85,83,91,104,106,89,103,92,109,104,124,134,130,137,145,
%U 149,151,116,112,128,145,158,151,152,130,119,127,167,196
%N Sum of digits of 5^n.
%C We can expect and conjecture that a(n) ~ 4.5*log_10(5)*n, but for n ~ 10^3..10^4 there are still fluctuations of +- 1%, e.g., a(10^3)/log_10(5) ~ 4538, a(10^4)/log_10(5) ~ 44518. Modulo 9, the sequence is periodic with period (1, 5, 7, 8, 4, 2) of length 6. No term is divisible by 3, a(n) = (-1)^n (mod 3). - _M. F. Hasler_, May 18 2017
%H Harry J. Smith, <a href="/A066001/b066001.txt">Table of n, a(n) for n = 0..1000</a>
%t Table[ Total@ IntegerDigits[5^n], {n, 0, 60}] (* _Robert G. Wilson v_ Oct 25 2006 *).
%t Table[Total[IntegerDigits[5^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) } { for (n=0, 1000, a=SumD(5^n); write("b066001.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 06 2009
%o (PARI) A066001=a(n)=sumdigits(5^n); \\ _Michel Marcus_, Sep 04 2014
%Y Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), A065713 (k=4), this sequence (k=5), A066002 (k=6), A066003 (k=7), A066004 (k=8), A065999 (k=9), A066005 (k=11), A066006 (k=12), A175527 (k=13).
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_, Dec 11 2001
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