A272531 Decimal expansion of C_2 (so named by S. Finch), a constant which is an analog of Niven's constant when mean of exponents is considered instead of maximum.

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

Offset

0,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.2 Meissel-Mertens constants (pp. 94-95) and Section 2.6 Niven's constant p.112.

Links

Table of n, a(n) for n=0..99.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 15.

Eric Weisstein's MathWorld, Niven's Constant

Formula

C_2 = C_1 (1 - M) - N, using Finch's notation, where C_1 is A136141, M A077761 and N A085548.

Example

0.1187309349576408430176668841155338623125786669962548878395960878789...

Mathematica

digits = 100;
C1 = NSum[PrimeZetaP[n], {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits] ;
M = EulerGamma - NSum[PrimeZetaP[n]/n, {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 3*digits] ;
N0 = PrimeZetaP[2];
C2 = C1 (1 - M) - N0;
RealDigits[C2, 10, digits][[1]]

Crossrefs

Cf. A033150, A077761, A085548, A136141.

Sequence in context: A329450 A203069 A343626 * A244684 A201742 A019764

Adjacent sequences: A272528 A272529 A272530 * A272532 A272533 A272534

Keyword

nonn,cons

Author

Jean-François Alcover, May 02 2016

Status

approved