A271780 - OEIS

A271780

Decimal expansion of Product_{p odd prime} 1-2/(p*(p-1)), a constant related to Artin's conjecture in the context of quadratic fields.

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

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OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.4 Artin's constant, p. 105.

LINKS

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

FORMULA

Equals (8/Pi^2)*A005597.

EXAMPLE

0.5351070126166387332839586518606321598586393391028...

MATHEMATICA

digits = 99; $MaxExtraPrecision = 600; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, 1, -2}, {0, 4, 6}, 2 m0]; r[n_Integer] := LR[[n]];

s[m_] := s[m] = NSum[-r[n] (PrimeZetaP[n] - 1/2^n)/n, {n, 2, m}, NSumTerms -> m0, WorkingPrecision -> 600] // 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(1-2/(p*(p-1)), 1, 3) \\ Amiram Eldar, Mar 11 2021

CROSSREFS

Cf. A005597, A217739 (8/Pi^2).

Sequence in context: A133658 A267445 A071050 * A176036 A194624 A239805

Adjacent sequences: A271777 A271778 A271779 * A271781 A271782 A271783

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Apr 15 2016

STATUS

approved