A238104 Sum of digits in periodic part of decimal expansion of 1/prime(n).

0, 3, 0, 27, 9, 27, 72, 81, 99, 126, 54, 9, 18, 90, 207, 63, 261, 270, 144, 126, 36, 54, 171, 198, 432, 18, 153, 225, 486, 504, 189, 585, 36, 207, 666, 306, 351, 360, 747, 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

Offset

1,2

Comments

Digit-sum of A060283(n).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007953(A060283(n)). - Michel Marcus, Mar 02 2014

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A060283, A002371, A238105, A238106.

Sequence in context: A360063 A009777 A138543 * A143769 A190963 A296436

Adjacent sequences: A238101 A238102 A238103 * A238105 A238106 A238107

Keyword

nonn,base

Author

Kozhukhov Vlad, Dec 04 2013

Extensions

Edited by David Applegate, Mar 01 2014

Status

approved