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Sum of digits in periodic part of decimal expansion of 1/prime(n).
4

%I #36 May 22 2017 03:36:30

%S 0,3,0,27,9,27,72,81,99,126,54,9,18,90,207,63,261,270,144,126,36,54,

%T 171,198,432,18,153,225,486,504,189,585,36,207,666,306,351,360,747,

%U 207,801,810,369,864,441,405,135,999,486,1026,1044,18,135,225,1152,1179,1206,18,324,126,621,657,675,612,1404,351

%N Sum of digits in periodic part of decimal expansion of 1/prime(n).

%C Digit-sum of A060283(n).

%H Michael De Vlieger, <a href="/A238104/b238104.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007953(A060283(n)). - _Michel Marcus_, Mar 02 2014

%e Prime(6) = 13, 1/13 = 0.076923076923076923076923..., the periodic part of which is 076923, whose digits add to 27 = a(6).

%e Since prime(n) must either divide or be coprime to 10, decimal expansions of prime(n) must either terminate or be purely recurrent, respectively. The only primes that divide 10 are prime(1) and prime(3), thus a(1) and a(3) = 0 as they have terminating decimal expansions. - _Michael De Vlieger_, May 20 2017

%t Table[Function[p, If[Divisible[10, p], 0, Total[RealDigits[1/p][[1, 1]]]]]@ Prime@ n, {n, 66}] (* _Michael De Vlieger_, May 20 2017 *)

%o (PARI) forprime(i=1,1e2,print1(sumdigits((10^iferr(znorder(Mod(10,i)),E,0)-1)/i)", ")) \\ _Lear Young_, Mar 01 2014

%Y Cf. A060283, A002371, A238105, A238106.

%K nonn,base

%O 1,2

%A _Kozhukhov Vlad_, Dec 04 2013

%E Edited by _David Applegate_, Mar 01 2014