A065478 Decimal expansion of Product_{p prime} (1 - p/(p^3-1)).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 106.

Links

Table of n, a(n) for n=0..97.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 155.

Yilan Hu and Carl Pomerance, The average order of elements in the multiplicative group of a finite field, involve, Vol. 5 (2012), No. 2, 229-236. See p. 8.

Sungjin Kim, Average results on the order of a modulo p, Journal of Number Theory, Vol. 169 (2016), pp. 353-368; arXiv preprint, arXiv:1509.01752 [math.NT], 2015.

Pär Kurlberg and Carl Pomerance, On a problem of Arnold: the average multiplicative order of a given integer, Algebra and Number Theory, Vol. 7, No. 4 (2013), pp. 981-999; alternative link.

Pieter Moree and Peter Stevenhagen, A two-variable Artin conjecture, Journal of Number Theory, Vol. 85, No. 2 (2000), pp. 291-304; arXiv preprint, arXiv:math/9912250 [math.NT], 1999.

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

P. J. Stephens, An average result for Artin's conjecture, Mathematika, Vol. 16, No. 2 (1969), pp. 178-188.

P. J. Stephens, Prime divisors of second-order linear recurrences. I,, Journal of Number Theory, Vol. 8, No. 3 (1976), pp. 313-332.

Eric Weisstein's World of Mathematics, Stephens' Constant.

Wikipedia, Stephens' constant.

Example

0.57595996889294543964316337549249669...

Mathematica

$MaxExtraPrecision = 100; m0 = 200; dm = 200; digits = 101; Clear[f]; f[m_] := f[m] = (slog = Normal[Series[Log[1 - p/(p^3 - 1)], {p, Infinity, m}]]; Exp[slog] /. Power[p, n_] -> PrimeZetaP[-n] // N[#, digits+10]&); f[m = m0]; Print[m, " ", f[m]]; f[m = m + dm]; While[Print[m, " ", f[m]]; RealDigits[f[m], 10, digits+5] != RealDigits[f[m - dm], 10, digits+5], m = m + dm]; RealDigits[f[m], 10, digits] // First (* Jean-François Alcover, Sep 15 2015 *)

Prog

(PARI) prodeulerrat(1 - p/(p^3-1)) \\ Amiram Eldar, Mar 17 2021

Crossrefs

Cf. A078079.

Sequence in context: A348052 A195498 A065746 * A109353 A247827 A205694

Adjacent sequences: A065475 A065476 A065477 * A065479 A065480 A065481

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 19 2001

Status

approved