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

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-4 expansion. - M. F. Hasler, Jul 04 2017

Examples

			0.079162851037850149671771117962208184613038569751878...
		

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).

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, 1/4^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

Formula

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

Extensions

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 04 2017