A157413 Decimal expansion of sum_{p = primes = A000040} 1/(p*2^p).

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

Offset

0,2

Links

Table of n, a(n) for n=0..104.

R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900, eq (66).

Formula

A002162 = sum_{n>=1} 1/(n*2^n) = 1/2 + this_constant_here + A157414 + equivalent terms of higher order k-almost primes.

Example

0.174087071760979362471993... = 1/(2*2^2)+1/(3*2^3)+1/(5*2^5)+1/(7*2^7)+... = sum_{i>=1} 1/(A000040(i)*A034785(i)).

Crossrefs

Sequence in context: A020790 A199955 A196624 * A258500 A243308 A293609

Adjacent sequences: A157410 A157411 A157412 * A157414 A157415 A157416

Keyword

cons,nonn

Author

R. J. Mathar, Feb 28 2009

Status

approved