%I A065876
%S A065876 1,3,3,7,13,21,31,43,18,73,91,111,17,47,183,211,241,133,57,343,381,47,
%T A065876 172,83,553,601,651,173,342,813,242,265,132,403,411,1191,1261,237,327,
%U A065876 1483,1561,1641,748,857,850,1981,684,463,413,2353,255,2551,593,1177,2863,
               123,3081,307,1288,3423
%N A065876 a(n) is the smallest m > n such that n^2+1 divides m^2+1.
%C A065876 a(n) exists because ((n^2-n+1)^2+1)= 0 mod(n^2+1). The set of n such 
               a(n) = n^2-n+1 is S=( 2, 3, 4, 5, 6, 7, 9, 11, 14, 15, ...)
%C A065876 a(n) = n^2-n+1 whenever n^2+1 is prime or twice a prime. Up to n=1000, 
               the only other n for which a(n) = n^2-n+1 are 7, 41 and 239. Is it 
               a coincidence that these are NSW primes (A088165)? - Franklin T. 
               Adams-Watters (FrankTAW(AT)Netscape.net), Oct 17 2006
%C A065876 It appears that the density of even numbers in this sequence approaches 
               a limit near 1/4. It appears that the density of even values for 
               indices where a(n) != n^2-n+1 is approaching a number near 1/4 and 
               based on the previous comment the density of n for which a(n) = n^2-n+1 
               is almost certainly 0. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Oct 17 2006
%H A065876 Franklin T. Adams-Watters, <a href="b065876.txt">Table of n, a(n) for 
               n = 0..1000</a>
%t A065876 Do[k = 1; While[m = (k^2 + 1)/(n^2 + 1); m < 2 || !IntegerQ[m], k++ ]; 
               Print[k], {n, 1, 40 } ]
%o A065876 (PARI) { for (n=0, 1000, a=n+1; while ((a^2 + 1)%(n^2 + 1) != 0, a++); 
               write("b065876.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Nov 03 2009]
%Y A065876 See also A088165, A005574, A002731.
%Y A065876 Sequence in context: A116880 A051123 A096188 this_sequence A095008 A134346 
               A049772
%Y A065876 Adjacent sequences: A065873 A065874 A065875 this_sequence A065877 A065878 
               A065879
%K A065876 nonn
%O A065876 0,2
%A A065876 Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 07 2001
%E A065876 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 11 2001
%E A065876 Further terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Oct 17 2006