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A275976 Decimal expansion of a constant relating to the density of Fibonacci integers. 0
5, 1, 5, 5, 1, 2, 4, 3, 4, 0, 0, 7, 4, 6, 4, 4, 0, 5, 5, 1, 4, 1, 6, 1, 9, 3, 3, 7, 5, 6, 5, 2, 2, 8, 2, 8, 7, 4, 8, 5, 7, 6, 0, 4, 5, 1, 8, 8, 1, 1, 0, 0, 2, 4, 8, 3, 1, 4, 3, 1, 1, 0, 7, 7, 6, 9, 7, 3, 5, 0, 2, 9, 8, 8, 6, 6, 9, 4, 6, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let F(x) be the number of Fibonacci integers, A178772, less than or equal to x. Then exp(c*sqrt(log x) - (log x)^e) < F(x) < exp(c*sqrt(log x) + (log x)^(1/6 + e)) for any e > 0, where c is this constant. Luca, Pomerance, & Wagner conjecture that 1/6 can be replaced by 0, and note that it can be replaced by 1/8 on a strong form of the abc conjecture.

LINKS

Table of n, a(n) for n=1..81.

Florian Luca, Carl Pomerance, Stephan Wagner, Fibonacci Integers, J. Number Theory 131 (2011), pp. 440-457. [conference version]

FORMULA

2*zeta(2)*sqrt(zeta(3)/zeta(6)/log(phi)) where phi = (1 + sqrt(5))/2 is the golden ratio.

EXAMPLE

5.1551243400746440551416193375652282874857604518811002483143110776973502988669...

MATHEMATICA

RealDigits[2 Zeta[2] Sqrt[Zeta[3]/Zeta[6]/Log[GoldenRatio]], 10, 81][[1]] (* Indranil Ghosh, Mar 19 2017 *)

PROG

(PARI) phi=(sqrt(5)+1)/2

2*zeta(2)*sqrt(zeta(3)/zeta(6)/log(phi))

CROSSREFS

Cf. A178772.

Sequence in context: A228639 A073226 A021198 * A306577 A143969 A198366

Adjacent sequences:  A275973 A275974 A275975 * A275977 A275978 A275979

KEYWORD

nonn,cons

AUTHOR

Charles R Greathouse IV, Aug 31 2016

STATUS

approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)