A125776 Continued fraction expansion of the Landau-Ramanujan constant (A064533).

0, 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 6, 4, 1, 1, 2, 4, 39, 1, 1, 3, 1, 2, 1, 3, 181, 2, 1, 103, 2, 1, 5, 1, 1, 1, 1, 6, 1, 7, 5, 1, 2, 1, 2, 2, 2, 2, 1, 21, 8, 1, 9, 2, 2, 4, 2, 6, 1, 4, 1, 1, 1, 1, 15, 1, 1, 10, 1, 7, 2, 1, 1, 2, 4, 2, 4, 1, 3, 1, 4, 1, 1, 23, 1, 1, 48, 1, 38, 1, 1, 1

Offset: 0

Author

Robert G. Wilson v, Dec 07 2006

Keywords

• cofr
• nonn

Comments

Increasing PQ's: 0, 1, 3, 4, 6, 15, 23, 39, 181, 386, 3389, 62656, ...

Examples

			k=0.7642236535892206629906987... = 0 + 1/(1 + 1/(3 + 1/(4 + 1/(6 + ...)))). - _Harry J. Smith_, Apr 23 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..9686

Crossrefs

Cf. A064533 (decimal expansion).

Programs

Mathematica

LandauRamanujan[n_] := N[Product[ ((1 - 2^(-2^k)) 4^(2^k) Zeta[2^k]/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^(2^(-k-1)), {k, n}]/Sqrt@2, 2^7]; ContinuedFraction@LandauRamanujan@8

Extensions

Offset changed by Andrew Howroyd, Aug 09 2024