A238114 Decimal expansion of constant 1 + B3 (or 1 + B_3) related to the Mertens constant.

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

Offset: 1

Author

N. J. A. Sloane, Mar 05 2014

Keywords

• nonn
• cons

Examples

			2.3325822757332208817658287760710277488384594890424226617871308997573400417193...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98

Links

• David Broadhurst, Table of n, a(n) for n = 1..300
• David Broadhurst, The Mertens constant ...
• David Broadhurst, 1000 digits
• Eric Weisstein's World of Mathematics, Mertens Constant

Crossrefs

Equals 1 + A083343, the latter being the main entry for this constant.

Programs

Mathematica

digits = 99;
B3 = EulerGamma - NSum[PrimeZetaP'[n], {n, 2, Infinity}, WorkingPrecision -> digits+50, NSumTerms -> 200];
RealDigits[1 + B3, 10, digits][[1]] (* Jean-François Alcover, Apr 26 2018 *)

Formula

B_3 = lim_{x->oo} ( log x - Sum_{p <= x} log p / p ). - Dick Boland, Mar 09 2008