A065489 - OEIS

A065489

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

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

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OFFSET

1,2

LINKS

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

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

FORMULA

1 divided by A065463. - R. J. Mathar, Mar 26 2011

EXAMPLE

1.419562880505485919317235861789735359... = 1/0.704442200999....

MATHEMATICA

$MaxExtraPrecision = 1200; digits = 99; terms = 1200; P[n_] := PrimeZetaP[n ]; LR = Join[{0, 0}, LinearRecurrence[{-2, 0, 1}, {2, -3, 6}, terms + 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. A065463, A078077.

Sequence in context: A125165 A259448 A200113 * A346404 A332385 A347968

Adjacent sequences: A065486 A065487 A065488 * A065490 A065491 A065492

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Nov 19 2001

STATUS

approved