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A123168 Continued fraction for c=sqrt(2)*(exp(sqrt(2))-1)/(exp(sqrt(2))+1). a(2n)=4n-3, a(2n+1)=8n-2. 2
0, 1, 6, 5, 14, 9, 22, 13, 30, 17, 38, 21, 46, 25, 54, 29, 62, 33, 70, 37, 78, 41, 86, 45, 94, 49, 102, 53, 110, 57, 118, 61, 126, 65, 134, 69, 142, 73, 150, 77, 158, 81, 166, 85, 174, 89, 182, 93, 190, 97, 198, 101, 206, 105, 214, 109, 222, 113 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This continued fraction shows exp(sqrt(2)) is irrational.

REFERENCES

J. Borwein and D. Bailey, Mathematics by experiment, plausible reasoning in the 21st Century, A. K. Peters, p. 77

LINKS

Table of n, a(n) for n=1..58.

FORMULA

Conjecture: a(n) = 2*a(n-2)-a(n-4) for n>5. G.f.: x^2*(1+6*x+3*x^2+2*x^3)/((1-x)^2*(1+x)^2). [Colin Barker, Apr 15 2012]

CROSSREFS

Sequence in context: A103132 A046627 A120114 * A119636 A101493 A188067

Adjacent sequences:  A123165 A123166 A123167 * A123169 A123170 A123171

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Oct 02 2006

STATUS

approved

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Last modified November 23 16:07 EST 2014. Contains 249851 sequences.