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 A374359 a(1) = 2, a(n) = 5 for n > 1. 2

%I #16 Jul 08 2024 06:24:22

%S 2,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%T 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

%N a(1) = 2, a(n) = 5 for n > 1.

%C Decimal expansion of 23/9, which is an approximation of the 5th root of 109 (A374357).

%C Simple continued fraction expansion of (1 + sqrt(29))/14 = (1 + A010484)/14.

%H Greg Martin and Winnie Miao, <a href="https://arxiv.org/abs/1409.2974">abc triples</a>, arXiv:1409.2974 [math.NT], 2014. See p. 5.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F G.f.: x*(2 + 3*x)/(1 - x).

%F a(n) = a(n-1) for n > 2.

%F E.g.f.: 5*exp(x) - 3*x - 5.

%e 2.555555555555555555555555555555555555555...

%t LinearRecurrence[{1},{2,5},100]

%Y Cf. A374357 (decimal expansion of the 5th root of 109), A374358 (continued fraction of the 5th root of 109).

%Y Cf. A010484.

%Y Essentially the same as A021022 and A010716.

%K nonn,cofr,cons,easy,less

%O 1,1

%A _Stefano Spezia_, Jul 06 2024

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Last modified September 19 12:32 EDT 2024. Contains 376012 sequences. (Running on oeis4.)