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

Author

Fred Lunnon and Simon Plouffe, Dec 11 1999

Keywords

• cofr
• nonn
• nice

Examples

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

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

Crossrefs

Cf. A005596.

Programs

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 *)

PARI

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