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A210395 Decimal expansion of continued fraction with quotients equal to Fermat numbers. 0
3, 1, 9, 7, 6, 7, 4, 9, 4, 4, 5, 8, 7, 6, 5, 5, 9, 3, 6, 4, 1, 1, 6, 2, 8, 9, 0, 2, 1, 7, 5, 2, 4, 4, 8, 0, 2, 1, 2, 7, 8, 3, 5, 2, 5, 4, 1, 4, 9, 1, 5, 7, 1, 9, 2, 5, 7, 5, 1, 4, 9, 3, 1, 6, 9, 9, 2, 9, 2, 8, 9, 3, 2, 1, 5, 9, 9, 2, 6, 8, 0, 0, 7, 9, 9, 5, 5, 7, 8, 7, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

A. Ya. Khinchin, Continued Fractions, Dover Publications, 1997.

M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, Springer, 2011.

LINKS

Table of n, a(n) for n=1..92.

Wikipedia, Continued fraction

Wikipedia, Fermat number

FORMULA

a(0).a(1)a(2)a(3)a(4)a(5)... = F_0 + 1/(F_1 + 1/(F_2 + 1/(F_3 + 1/(F_4 + ...)))) = [F_0,F_1,F_2,F_3,F_4,...] where a(0).a(1)a(2)a(3)a(4)... is a decimal representation of the continued fraction [F_0,F_1,F_2,F_3,F_4,...] where F_0, F_1,... are Fermat numbers.

EXAMPLE

3.19767494... = 3 + 1/(5 + 1/(17 + 1/(257 + 1/(65537 + ...))))

MATHEMATICA

FromContinuedFraction[{3, 5, 17, 257, 65537, 4294967297, 18446744073709551617}] (* for better precision, enter next Fermat numbers *)

PROG

(PARI) s=3; forstep(n=log(default(realprecision)*log(10)\log(2))\log(2), 1, -1, s=1/(2.^(2^n)+s+1)); s \\ Charles R Greathouse IV, Mar 21 2012

CROSSREFS

Cf. A000215.

Sequence in context: A231902 A143495 A245789 * A019770 A136320 A201840

Adjacent sequences:  A210392 A210393 A210394 * A210396 A210397 A210398

KEYWORD

nonn,cons

AUTHOR

Algirdas Javtokas, Mar 21 2012

EXTENSIONS

Offset changed by Bruno Berselli, May 14 2012

STATUS

approved

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Last modified May 26 19:32 EDT 2019. Contains 323597 sequences. (Running on oeis4.)