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A125776 Continued fraction expansion of the Landau-Ramanujan constant (A064533). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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 = 1..9687

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.

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

STATUS

approved

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Last modified January 23 01:55 EST 2018. Contains 298093 sequences.