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%I #16 Feb 13 2013 23:58:30
%S 5,12,16,20,64,76,49,100,112,64,136,148,160,172,184,105,120,220,120,
%T 244,256,121,280,292,161,316,144,176,352,364,221,217,400,217,424,436,
%U 232,225,472,484,496,288,273,532,225,288,253,580,352,604,616,276,640
%N Minimal k >= 5n such that n^2 + 2nk + k is a perfect square.
%C Without any restriction, trivially, a(n)=0 and, if to consider a(n) positive, then, again trivially, a(n)=1. Without the restriction k >= 5n, we have a(n)=4*n+1; on the other hand, if to require a(n)>=5*n and in addition a(n+1)>a(n), then we obtain sequence 5,12,16,20 and, beginning with n=5, we have progression 64+12*(n-5).
%t Table[k = 5*n; While[! IntegerQ[Sqrt[n^2 + 2*n*k + k]], k++]; k, {n, 100}] (* _T. D. Noe_, May 18 2012 *)
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, May 13 2012
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