A272030 Decimal expansion of C = log(2*Pi) + B_3 (where B_3 is A083343), one of Euler totient constants.

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

Offset: 1

Author

Jean-François Alcover, Apr 25 2016

Keywords

• nonn
• cons

Examples

			3.17045934214256636532648824888226302856125443631798948742143398...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.7 Euler totient constants, p. 117.

Crossrefs

Cf. A001620, A005596, A065484, A065485, A080130, A082695, A082695, A083343.

Programs

Mathematica

digits = 98; B3 = EulerGamma - NSum[PrimeZetaP'[n], {n, 2, Infinity}, WorkingPrecision -> 2 digits, NSumTerms -> 200]; RealDigits[Log[2 Pi] + B3, 10, digits][[1]]

Formula

C = log(2*Pi) + EulerGamma - Sum_{n >= 2} P'(n), where P'(n) is the prime zeta P function derivative.