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

0,3

Comments

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

Links

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

Example

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

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

Crossrefs

Cf. A064533 (decimal expansion).

Sequence in context: A275979 A246859 A122601 * A066977 A007551 A161012

Adjacent sequences: A125773 A125774 A125775 * A125777 A125778 A125779

Keyword

cofr,nonn

Author

Robert G. Wilson v, Dec 07 2006

Extensions

Offset changed by Andrew Howroyd, Aug 09 2024

Status

approved