cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A132797 Decimal expansion of Sum_{n >= 1} 1/5^prime(n).

This page as a plain text file.
%I A132797 #17 Aug 11 2020 09:55:12
%S A132797 0,4,8,3,3,2,8,2,1,3,0,0,5,6,3,2,3,2,6,9,1,6,6,3,4,7,1,2,5,1,5,6,6,5,
%T A132797 9,6,5,2,2,7,0,2,3,4,1,0,3,4,0,1,5,8,2,7,2,2,9,4,9,6,7,7,4,6,8,3,9,2,
%U A132797 7,9,1,6,6,9,7,5,0,9,6,0,6,5,1,5,2,7,2,3,8,6,6,3,8,6,6,1,6,0
%N A132797 Decimal expansion of Sum_{n >= 1} 1/5^prime(n).
%C A132797 Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-5 expansion. - _M. F. Hasler_, Jul 04 2017
%F A132797 From _Amiram Eldar_, Aug 11 2020: (Start)
%F A132797 Equals Sum_{k>=1} 1/A057902(k).
%F A132797 Equals 4 * Sum_{k>=1} pi(k)/5^(k+1), where pi(k) = A000720(k). (End)
%e A132797 0.0483328213005632326916634712515665965227023410340158272294967746839279...
%o A132797 (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 A132797 (PARI) suminf(n=1, 1/5^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 A132797 Cf. A000720, A051006 (analog for base 2), A057902, A132800 (analog for base 3), A132806 (analog for base 4), A010051 (characteristic function of the primes), A132817 (base 6).
%K A132797 cons,nonn
%O A132797 0,2
%A A132797 _Cino Hilliard_, Nov 17 2007
%E A132797 Offset corrected _R. J. Mathar_, Jan 26 2009
%E A132797 Edited by _M. F. Hasler_, Jul 04 2017