A065416 Decimal expansion of Product_{p prime} (1-1/(p^5-p^4)).

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

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..98.

G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Example

0.93126518416000433438923720555067698...

Mathematica

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

Prog

(PARI) prodeulerrat(1-1/(p^5-p^4)) \\ Amiram Eldar, Mar 12 2021

Crossrefs

Cf. A005596, A065414, A065415.

Sequence in context: A134897 A010159 A097528 * A093312 A154629 A333182

Adjacent sequences: A065413 A065414 A065415 * A065417 A065418 A065419

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 15 2001

Status

approved