A132797 Decimal expansion of Sum_{n >= 1} 1/5^prime(n).

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

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-5 expansion. - M. F. Hasler, Jul 04 2017

Examples

			0.0483328213005632326916634712515665965227023410340158272294967746839279...
		

Crossrefs

Cf. A000720, A051006 (analog for base 2), A057902, A132800 (analog for base 3), A132806 (analog for base 4), A010051 (characteristic function of the primes), A132817 (base 6).

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, 1/5^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

From Amiram Eldar, Aug 11 2020: (Start)

Equals Sum_{k>=1} 1/A057902(k).

Equals 4 * Sum_{k>=1} pi(k)/5^(k+1), where pi(k) = A000720(k). (End)

Extensions

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 04 2017