A132822 - OEIS

%I #15 Aug 11 2020 10:00:42

%S 0,2,3,3,8,4,3,2,8,9,6,0,3,5,3,7,3,9,9,0,9,8,5,9,8,2,2,4,9,5,9,1,2,3,

%T 7,3,4,8,9,3,4,0,9,3,5,9,3,5,9,4,4,8,6,9,6,1,9,9,8,2,8,8,4,6,5,6,5,2,

%U 3,5,6,8,2,7,5,4,6,8,0,5,1,2,1,2,1,3,6,2,1,8,6,3,1,0,7,6,2,7

%N Decimal expansion of Sum_{n >= 1} 1/7^prime(n).

%C Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-7 expansion. - _M. F. Hasler_, Jul 05 2017

%F From _Amiram Eldar_, Aug 11 2020: (Start)

%F Equals Sum_{k>=1} 1/A269327(k).

%F Equals 6 * Sum_{k>=1} pi(k)/7^(k+1), where pi(k) = A000720(k). (End)

%e 0.023384328960353739909859822495912373489340935935944869619982884656523568...

%o (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 (PARI) suminf(n=1, 1/7^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 05 2017

%Y Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132806 (analog for base 4), A132797 (analog for base 5), A132817 (analog for base 6), A010051 (characteristic function of the primes), A132799 (base 8), A269327.

%K cons,nonn

%O 0,2

%A _Cino Hilliard_, Nov 17 2007

%E Offset corrected by _R. J. Mathar_, Feb 05 2009

%E Edited by _M. F. Hasler_, Jul 05 2017