A307372 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).

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, 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

Offset: 1

Author

Wolfdieter Lang, Apr 19 2019

Keywords

• nonn

Comments

This is a subsequence of A226166. See the formula.

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).

Crossrefs

Cf. A000037, A079896, A226166, A324251.

Formula

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.

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