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
Examples
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
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
PARI
forprime(i=1,1e2,print1(sumdigits((10^iferr(znorder(Mod(10,i)),E,0)-1)/i)", ")) \\ Lear Young, Mar 01 2014
Formula
Extensions
Edited by David Applegate, Mar 01 2014
Comments