A184083 Decimal expansion of product_{p=primes} (1+1/2^p).

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

Offset

1,2

Comments

Inverse of the constant A184084.

Links

Table of n, a(n) for n=1..79.

Formula

Equals product_{p in A000040} (1+2^(-p)) = sum_{n>=0} A000586(n)/2^n.

Example

(1+1/2^2) *(1+1/2^3) *(1+1/2^5) *(1+1/2^7) *(1+1/2^11)* .... = 1.4624312190069598013...

Mathematica

RealDigits[Times@@(1+1/2^Prime[Range[100]]), 10, 120][[1]] (* Harvey P. Dale, Sep 28 2013 *)

Prog

(PARI) prodeuler(p=2, 1e6, 1.+(1.>>p)) \\ Charles R Greathouse IV, Aug 09 2022

Crossrefs

Sequence in context: A077158 A059854 A155991 * A244993 A160502 A010669

Adjacent sequences: A184080 A184081 A184082 * A184084 A184085 A184086

Keyword

cons,nonn

Author

R. J. Mathar, Jan 09 2011

Status

approved