A307372 - OEIS

%I #16 Feb 19 2021 10:41:26

%S 1,1,1,1,2,1,1,1,1,5,2,1,1,1,3,1,3,3,2,1,1,1,2,5,1,4,2,2,2,1,1,1,1,1,

%T 3,1,5,4,3,6,2,1,1,1,3,5,3,2,1,3,7,3,2,11,2,1,1,1,5,1

%N One half of the row length of A324251: one half of the length of the reduced principal cycle for discriminant 4*D(n), with D(n) = A000037(n).

%C This is a subsequence of A226166. See the formula.

%C For details on the cycles for the principal form F_p(n) = FR(n), the first reduced form of the not reduced Pell form F(n) = [1, 0, -D(n)], see A324251, also for references and a W. Lang link with Table 1, last column LCR(n) = 2*a(n).

%F a(n) equals one half of the length of the reduced principal cycle of discriminant 4*D(n), with D(n) = A000037(n)), for n >= 1.

%F a(n) =  A226166(e(n)), where e(n) is the n-th even term of A079896, for n >= 1.

%Y Cf. A000037, A079896, A226166, A324251.

%K nonn

%O 1,5

%A _Wolfdieter Lang_, Apr 19 2019