A184085 Decimal expansion of product_{p=primes} (1-1/(2^p-1)).

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

Offset: 0

Author

R. J. Mathar, Jan 09 2011

Keywords

• cons
• nonn

Examples

			(1-1/3) *(1-1/7) *(1-1/31) *(1-1/127) *(1-1/2047) * ... = 0.5483008312820984076776404...
		

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 17.

Programs

Mathematica

digits = 103; m0 = 10; dm = 10; f[m_] := f[m] = Product[p = Prime[n]; 1 - 1/(2^p - 1), {n, 1, m}]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits+2] != RealDigits[f[m - dm], 10, digits+2], m = m + dm]; RealDigits[f[m], 10, digits] // First (* Jean-François Alcover, Oct 14 2014 *)

Formula

Equals product_{p in A000040} (1-1/(2^p-1)) = product_{n>=1} (1-1/A001348(n)).

Extensions

More digits from Jean-François Alcover, Oct 14 2014