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A271869 Decimal expansion of Matthews' constant C_3, an analog of Artin's constant for primitive roots. 1
0, 6, 0, 8, 2, 1, 6, 5, 5, 1, 2, 0, 3, 0, 5, 0, 8, 6, 0, 0, 5, 6, 3, 2, 2, 7, 5, 4, 6, 1, 9, 2, 0, 8, 5, 5, 4, 3, 1, 3, 3, 7, 3, 7, 3, 4, 7, 5, 7, 6, 7, 9, 4, 1, 9, 8, 2, 6, 4, 3, 4, 0, 3, 1, 5, 0, 4, 0, 8, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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..70.

FORMULA

C_3 = Product_{p prime} 1 - (p^3 - (p - 1)^3)/(p^3*(p - 1)).

EXAMPLE

0.0608216551203050860056322754619208554313373734757679419826434...

MATHEMATICA

digits = 70; $MaxExtraPrecision = 1000; m0 = 2000; dm = 200; Clear[s]; LR =

LinearRecurrence[{2, 2, -6, 4, -1}, {0, 6, 0, 22, 5}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> 2 m0, WorkingPrecision -> digits+10] // 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]; Join[{0}, RealDigits[ s[m], 10, digits][[1]]]

CROSSREFS

Cf. A005596, A065414, A065415, A065416, A271780, A271798.

Sequence in context: A279929 A244812 A083680 * A010491 A257095 A159845

Adjacent sequences:  A271866 A271867 A271868 * A271870 A271871 A271872

KEYWORD

nonn,cons,more

AUTHOR

Jean-Fran├žois Alcover, Apr 16 2016

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)