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%I #3 Mar 30 2012 17:27:56
%S 110443,6826318,3379649772,61012922706,1019349744435,287369842623,
%T 11331029931180,71294762793847,239822883201307,923990886302412,
%U 2369608176604944,3156215819652023,521749964271465,2026364722410364
%N Smallest k such that k^2+1 is divisible by A002144(n)^8.
%e a(1) = 110443 since A002144(1) = 5, 110443^2+1 = 12197656250 = 2*5^8*13*1201 and for no k < 110443 does 5^8 divide k^2+1. a(3) = 3379649772 since A002144(3) = 17, 3379649772^2+1 = 11422032581379651985 = 5*13*17^8*97*259697 and for no k < 3379649772 does 17^8 divide k^2+1.
%o (PARI) {e=8; forprime(p=2, 40, if(p%4==1, q=p^e; m=q; while(!issquare(m-1, &n), m=m+q); print1(n, ",")))}
%Y Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298, A145299, A145871, A145873.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Oct 22 2008
%E More terms from _Klaus Brockhaus_, Nov 12 2008
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