A049457 - OEIS

A049457

Least positive integer k such that the number having periodic continued fraction [ 1,m,1,m,1,m,... ] is of form (a+b*sqrt(k))/c, where a,b,c are positive integers.

5, 3, 21, 2, 5, 15, 77, 6, 13, 35, 165, 3, 221, 7, 285, 5, 357, 11, 437, 30, 21, 143, 69, 42, 29, 195, 93, 14, 957, 255, 1085, 2, 1221, 323, 1365, 10, 1517, 399, 1677, 110, 205, 483, 2021, 33, 5, 23, 2397, 39, 53, 3, 2805, 182, 3021, 87, 3245, 210, 3477, 899, 413

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OFFSET

1,1

COMMENTS

Squarefree factors of k^2+2k-3. - Artur Jasinski, May 19 2008

LINKS

Table of n, a(n) for n=1..59.

FORMULA

Least positive integer of the form m(m+4)/(w^2), where m and w are positive integers.

PROG

(PARI) a(n)=if(n<1, 0, core(n^2+4*n))

CROSSREFS