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

0,2

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

Links

Table of n, a(n) for n=0..97.

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)

Example

0.023384328960353739909859822495912373489340935935944869619982884656523568...

Prog

(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

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.

Sequence in context: A096714 A078035 A295725 * A347823 A185297 A329803

Adjacent sequences: A132819 A132820 A132821 * A132823 A132824 A132825

Keyword

cons,nonn

Author

Cino Hilliard, Nov 17 2007

Extensions

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

Edited by M. F. Hasler, Jul 05 2017

Status

approved