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%I #23 May 20 2017 14:48:17
%S 1,4,16,19,22,25,37,40,34,46,67,52,55,58,97,73,85,88,91,85,115,91,121,
%T 106,109,121,133,118,121,133,163,184,169,181,193,169,172,175,178,199,
%U 193,214,226,238,169,190,247,241,208,247,232,253,292,241,316,292,268,271,301,286,298,337,304,325
%N Digit sum of 13^n.
%C It is surprising that many values repeat twice (for 85, 91, 121, 133, 169 this happens at a(n) = a(n+3) (but 169 occurs later for a third time), for 193, 241, 292, ... the second occurrence comes later) while many other values never occur. Is there a simple explanation? - _M. F. Hasler_, May 18 2017
%H Vincenzo Librandi, <a href="/A175527/b175527.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A007953(A001022(n)). - _Michel Marcus_, Nov 01 2013
%F a(n) ~ 4.5*log_10(13)*n ~ 5.0127*n (conjectured). - _M. F. Hasler_, May 18 2017
%t Table[Total[IntegerDigits[13^k]], {k,0,1000}]
%o (PARI) a(n)=sumdigits(13^n); \\ _Michel Marcus_, Nov 01 2013
%Y Cf. A001022, A175528, A175525.
%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), A065999 (k=9), A066005 (k=11), A066006 (k=12), this sequence (k=13).
%K base,nonn
%O 0,2
%A _N. J. A. Sloane_, Dec 03 2010