A065415 Decimal expansion of Product_{p prime} (1-1/(p^4-p^3)).

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

Offset: 0

Author

N. J. A. Sloane, Nov 15 2001

Keywords

• cons
• nonn

Examples

			0.85654044485354217442616798413595388...
		

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 over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011, constant A_1^(3) table 3.
• G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Crossrefs

Cf. A005596, A065414, A065416.

Programs

Mathematica

digits = 99; $MaxExtraPrecision = 400; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, -1, 0, 1, -1}, {0, 0, 0, 4, 5, 6}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 400] // 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 15 2016 *)

PARI

prodeulerrat(1-1/(p^4-p^3)) \\ Amiram Eldar, Mar 13 2021