A065414 Decimal expansion of rank 2 Artin constant Product_{p prime} (1-1/(p^3-p^2)).

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

Offset: 0

Author

N. J. A. Sloane, Nov 15 2001

Keywords

• cons
• nonn

Examples

			0.697501358496365903284670350820922924...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4, p. 105.

Links

• R. J. Mathar, Hardy-Littlewood constants embedded into infinite products.., arxiv:0903.2514 [math.NT], 2009-2011, variable A_1^(2).
• G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]
• Index entries for sequences related to Artin's conjecture.

Crossrefs

Cf. A005596, A065417.

Programs

Mathematica

digits = 99; m0 = 1000; dm = 100; Clear[s]; r[n_] := RootSum[-1 - #^2 + #^3 &, #^n&] - 1; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 300] // Exp; s[m0]; s[m = m0 + dm]; While[RealDigits[s[m], 10, digits][[1]] != RealDigits[s[m - dm], 10, digits][[1]], Print[m]; m = m + dm]; RealDigits[s[m], 10, digits][[1]] (* Jean-François Alcover, Apr 14 2016 *)

PARI

prodeulerrat(1-1/(p^3-p^2)) \\ Amiram Eldar, Mar 12 2021