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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. 0

%I #7 Apr 30 2014 01:37:51

%S 5,3,21,2,5,15,77,6,13,35,165,3,221,7,285,5,357,11,437,30,21,143,69,

%T 42,29,195,93,14,957,255,1085,2,1221,323,1365,10,1517,399,1677,110,

%U 205,483,2021,33,5,23,2397,39,53,3,2805,182,3021,87,3245,210,3477,899,413

%N 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.

%C Squarefree factors of k^2+2k-3. - _Artur Jasinski_, May 19 2008

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

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

%K nonn

%O 1,1

%A _Clark Kimberling_

%E More terms from _Michael Somos_, Oct 28, 2002

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Last modified April 30 20:43 EDT 2024. Contains 372141 sequences. (Running on oeis4.)