cp's OEIS Frontend

A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n).

%I A132817 #18 Aug 11 2020 10:00:27
%S A132817 0,3,2,5,3,9,5,8,3,3,0,8,5,2,5,5,4,4,0,4,9,2,6,0,0,5,0,7,8,1,2,7,4,1,
%T A132817 8,1,1,9,2,9,8,6,0,7,6,6,1,7,5,7,8,0,9,8,8,8,7,6,6,4,6,1,0,0,9,9,0,7,
%U A132817 6,7,7,3,8,3,1,3,0,3,9,1,5,1,6,3,3,8,8,0,9,3,4,8,0,6,3,5,4,1
%N A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n).
%C A132817 Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-6 expansion. - _M. F. Hasler_, Jul 05 2017
%H A132817 Vincenzo Librandi, <a href="/A132817/b132817.txt">Table of n, a(n) for n = 0..1110</a>
%F A132817 Equals 5 * Sum_{k>=1} pi(k)/6^(k+1), where pi(k) = A000720(k). - _Amiram Eldar_, Aug 11 2020
%e A132817 0.032539583308525544049260050781274181192986076617578098887664610099...
%t A132817 Join[{0}, RealDigits[FromDigits[{{Table[If[PrimeQ[n], 1, 0], {n, 370}]}, 0}, 6], 10, 111][[1]]] (* _Vincenzo Librandi_, Jul 05 2017 *)
%o A132817 (PARI) /* Sum of 1/m^p for primes p */ sumnp(n,m) = { local(s=0,a,j); for(x=1,n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3,n, print1(eval(a[j])",") ) }
%o A132817 (PARI) suminf(n=1, 1/6^prime(n)) \\ Then: digits(%\.1^default(realprecision))[1..-3] to remove the last 2 digits. N.B.: Functions sumpos() and sumnum() yield much less accurate results. - _M. F. Hasler_, Jul 04 2017
%Y A132817 Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132806 (analog for base 4), A132797 (analog for base 5), A132822 (analog for base 7), A010051 (characteristic function of the primes), A000040 (the primes).
%K A132817 cons,nonn
%O A132817 0,2
%A A132817 _Cino Hilliard_, Nov 17 2007
%E A132817 Offset corrected _R. J. Mathar_, Jan 26 2009
%E A132817 Edited by _M. F. Hasler_, Jul 05 2017