A132806 Decimal expansion of Sum_{n >= 1} 1/4^prime(n).

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

Offset

0,2

Comments

Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-4 expansion. - M. F. Hasler, Jul 04 2017

Links

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

Formula

Equals 3 * Sum_{k>=1} pi(k)/4^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020

Example

0.079162851037850149671771117962208184613038569751878...

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, 1/4^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

Crossrefs

Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132797 (analog for base 5), A010051 (characteristic function of the primes), A000040 (the primes).

Sequence in context: A086318 A244674 A130834 * A016629 A154203 A055676

Adjacent sequences: A132803 A132804 A132805 * A132807 A132808 A132809

Keyword

cons,nonn

Author

Cino Hilliard, Nov 17 2007

Extensions

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 04 2017

Status

approved