A132799 Decimal expansion of the convergent to the sum of (1/8)^p where p ranges over the set of prime numbers.

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

Offset: 0

Author

Cino Hilliard, Nov 17 2007

Keywords

• cons
• nonn

Examples

			0.01760911...
		

Crossrefs

Cf. A000720, A132822 (base 7), A132821 (base 9).

Programs

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])",") ) }

Formula

Equals 7 * Sum_{k>=1} pi(k)/8^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020

Extensions

Offset corrected R. J. Mathar, Jan 26 2009