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%I #43 Feb 20 2024 18:37:49
%S 31,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,
%T 62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,
%U 62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62
%N Continued fraction for sqrt(962).
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Con#constant">Index entries for eventually constant sequences</a>.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F G.f.: 31*(1+x)/(1-x). - _Colin Barker_, Aug 11 2012
%F From _Elmo R. Oliveira_, Feb 16 2024: (Start)
%F a(n) = 62 for n >= 1.
%F E.g.f.: 62*exp(x) - 31.
%F a(n) = 31*A040000(n). (End)
%e 31 + 1/(62 + 1/(62 + 1/(62 + 1/(62 + ...)))) = sqrt(962).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(962)),confrac);
%t PadRight[{31},100,62] (* _Harvey P. Dale_, Sep 18 2012 *)
%Y Cf. A042860/A042861 (convergents).
%Y 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,...)).
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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