A048296 Continued fraction for Artin's constant.

0, 2, 1, 2, 14, 1, 1, 2, 3, 5, 1, 3, 1, 5, 1, 1, 2, 3, 5, 46, 2, 2, 4, 4, 2, 1, 6, 1, 1, 4, 2, 2, 1, 109, 1, 1, 4, 9, 3, 45, 8, 4, 1, 2, 1, 13, 13, 1, 1, 2, 1, 1, 2, 1, 4, 2, 3, 1, 17, 1, 1, 1, 6, 42, 1, 3, 1, 1, 4, 1, 1, 1, 1, 1, 2, 4, 5, 4, 1, 26, 1, 1, 74, 1, 1, 2, 1, 2, 2, 1, 1, 10, 1

Offset

0,2

References

See A005596 for further references.

Links

Harry J. Smith, Table of n, a(n) for n = 0..995

Index entries for sequences related to Artin's conjecture

Example

artin = 0.37395581361920228805... = 0 + 1/(2 + 1/(1 + 1/(2 + 1/(14 + ...)))). - Harry J. Smith, Apr 23 2009

Mathematica

digits = 105; m0 = 1000; dm = 100; Clear[s]; r[n_] := -1 + Fibonacci[n-1] + Fibonacci[n+1]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> m0, WorkingPrecision -> 400] // 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]; A = s[m]; ContinuedFraction[A, 93] (* Jean-François Alcover, Apr 15 2016 *)

Prog

(PARI) contfrac(prodeulerrat(1-1/(p^2-p))) \\ Amiram Eldar, Mar 12 2021

Crossrefs

Cf. A005596.

Sequence in context: A052579 A266314 A153908 * A016542 A242085 A007402

Adjacent sequences: A048293 A048294 A048295 * A048297 A048298 A048299

Keyword

cofr,nonn,nice

Author

Fred Lunnon and Simon Plouffe, Dec 11 1999

Status

approved