A132822 Decimal expansion of Sum_{n >= 1} 1/7^prime(n).

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, 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, 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

Offset: 0

Author

Cino Hilliard, Nov 17 2007

Keywords

• cons
• nonn

Comments

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

Examples

			0.023384328960353739909859822495912373489340935935944869619982884656523568...
		

Crossrefs

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.

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])",") ) }

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

Formula

From Amiram Eldar, Aug 11 2020: (Start)

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

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

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

Edited by M. F. Hasler, Jul 05 2017