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a(n) = k that produces the smallest integer m > 1 of the form m = (k^2 + n)/(n^2 + k).
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%I #19 Aug 18 2015 03:56:42

%S 5,5,10,10,26,37,12,65,30,27,38,145,109,197,226,62,290,129,108,401,

%T 442,69,56,577,130,48,730,464,105,103,300,220,1090,363,147,222,194,

%U 1445,184,902,1682,387,588,390,391,263,258,133,350,2501,2119,1484,549,2917

%N a(n) = k that produces the smallest integer m > 1 of the form m = (k^2 + n)/(n^2 + k).

%C The function m(k) is a monotonically increasing function of k if n is held constant. Therefore the implementation may scan k upwards until the first integer m is found. - _R. J. Mathar_, Aug 07 2014

%H Vincenzo Librandi, <a href="/A066256/b066256.txt">Table of n, a(n) for n = 2..250</a>

%p A066256 := proc(n)

%p local k,f ;

%p for k from 1 do

%p f := (k^2+n)/(n^2+k) ;

%p if f > 1 and type(f,'integer') then

%p return k;

%p end if;

%p end do:

%p end proc: # _R. J. Mathar_, Aug 07 2014

%t Do[k = 1; While[m = (k^2 + n)/(n^2 + k); !IntegerQ[m] || m == 1, k++ ]; Print[k], {n, 2, 75} ]

%Y Cf. A066257.

%K nonn

%O 2,1

%A _Benoit Cloitre_, Dec 31 2001

%E More terms from _Robert G. Wilson v_, Jan 03 2002