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A225204
Numerators of convergents to the square root of the golden ratio.
7
1, 4, 5, 14, 159, 491, 2614, 3105, 33664, 36769, 107202, 572779, 1825539, 9700474, 11526013, 32752500, 142536013, 175288513, 317824526, 810937565, 3561574786, 182451251651, 186012826437, 926502557399, 2039017941235, 5004538439869, 157179709577174
OFFSET
0,2
FORMULA
a(n) = A331692(n)*a(n-1) + a(n-2) for n >= 2. - Jianing Song, Aug 18 2022
EXAMPLE
1, 4/3, 5/4, 14/11, 159/125, 491/386, 2614/2055, 3105/2441, ... = A225204/A225205
MATHEMATICA
Numerator[Convergents[Sqrt[GoldenRatio], 20]]
CROSSREFS
Cf. A001622, A139339, A331692, A225205 (denominators).
Sequence in context: A042535 A222489 A222501 * A363817 A308095 A321348
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, May 01 2013
STATUS
approved