A065488 Decimal expansion of Product_{p prime} (1 + 1/(p^2-p-1)).

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

Offset

1,1

Comments

This is 1/Artin's constant, see A005596.

Links

Table of n, a(n) for n=1..99.

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

Example

2.67411272557002150896041183...

Mathematica

$MaxExtraPrecision = 1200; digits = 99; terms = 1200; P[n_] := PrimeZetaP[n ]; LR = Join[{0, 0}, LinearRecurrence[{2, 0, -1}, {2, 3, 6}, term+10]]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)

Prog

(PARI) prodeulerrat(1 + 1/(p^2-p-1)) \\ Amiram Eldar, Mar 15 2021

Crossrefs

Cf. A005596, A048296, A351219.

Sequence in context: A329246 A201891 A198430 * A016591 A021793 A365256

Adjacent sequences: A065485 A065486 A065487 * A065489 A065490 A065491

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 19 2001

Status

approved