A040930 Continued fraction for sqrt(962).
31, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62
Offset: 0
Examples
31 + 1/(62 + 1/(62 + 1/(62 + 1/(62 + ...)))) = sqrt(962).
Links
Crossrefs
Continued fraction for sqrt(a^2+1) = (a, 2a, 2a, 2a....): A040000 (contfrac(sqrt(2)) = (1,2,2,...)), A040002, A040006, A040012, A040020, A040030, A040042, A040056, A040072, A040090, A040110 (contfrac(sqrt(122)) = (11,22,22,...)), A040132, A040156, A040182, A040210, A040240, A040272, A040306, A040342, A040380, A040420 (contfrac(sqrt(442)) = (21,42,42,...)), A040462, A040506, A040552, A040600, A040650, A040702, A040756, A040812, A040870 (contfrac(sqrt(901)) = (30,60,60,...)).
Programs
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Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(962)),confrac);
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Mathematica
PadRight[{31},100,62] (* Harvey P. Dale, Sep 18 2012 *)
Formula
G.f.: 31*(1+x)/(1-x). - Colin Barker, Aug 11 2012
From Elmo R. Oliveira, Feb 16 2024: (Start)
a(n) = 62 for n >= 1.
E.g.f.: 62*exp(x) - 31.
a(n) = 31*A040000(n). (End)