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

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

Sequence in context: A298098 A248256 A369039 * A061037 A070262 A171621

Adjacent sequences: A049454 A049455 A049456 * A049458 A049459 A049460

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Michael Somos, Oct 28, 2002

Status

approved