A132800 Decimal expansion of Sum_{n >= 1} 1/3^prime(n).

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

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-3 expansion. - M. F. Hasler, Jul 04 2017.

Examples

			0.15272690272572247152817541874425912430342364271463298508628837536732...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000720, A051006 (analog for base 2), A132797 (analog for base 5), A010051 (characteristic function of the primes), A057901, A132806 (base 4).

Programs

Mathematica

RealDigits[Sum[1/3^Prime[k], {k, 100}], 10, 100][[1]] (* Vincenzo Librandi, Jul 05 2017 *)

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=3,100, print1(eval(a[j])",") ) }

PARI

suminf(n=1,1/3^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/A057901(k).

Equals 2 * Sum_{k>=1} pi(k)/3^(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