A077142 Decimal expansion of b = log(2*Pi) - 1 - gamma/2.

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

Offset

0,1

Comments

Arises in the Riemann zeta function's expression (Hadamard product): zeta(s) = exp(b*s)/(2*(s-1)*Gamma(s/2+1))*Product(r, (1-s/r)^exp(s/r)) where r runs through the zeros.

References

A. E. Ingham, The distribution of prime numbers, Cambridge, 1932, p. 58.

Links

Table of n, a(n) for n=0..103.

Eric Weisstein's World of Mathematics, Hadamard Product

Index entries for zeta function.

Formula

b = 0.54926923395857905325740342777003406420171527930560...

Mathematica

RealDigits[Log[2Pi]-1-EulerGamma/2, 10, 120][[1]] (* Harvey P. Dale, Nov 05 2011 *)

Prog

(PARI) log(2*Pi)-1-Euler/2 \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Cf. A074760.

Sequence in context: A097943 A241420 A386009 * A156057 A125057 A021186

Adjacent sequences: A077139 A077140 A077141 * A077143 A077144 A077145

Keyword

cons,nonn

Author

Benoit Cloitre, Nov 29 2002

Status

approved