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%I #8 Aug 16 2019 16:04:49
%S 144,390,856,1746,1814,1924,2170,2526,2636,2704,2814,3170,3416,3594,
%T 3704,3950,4060,4306,4840,4950,5306,5484,6374,6620,6730,7086,7154,
%U 7264,7866,7976,8044,8154,8400,8756,8866,9044,9400,9646,9824,10180,10290,11070,11426
%N Numbers n such that the smallest prime divisor of n^2+1 is 89.
%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(11).
%C a(n)== 34 or 144 (mod 178).
%H Amiram Eldar, <a href="/A248551/b248551.txt">Table of n, a(n) for n = 1..10000</a>
%e 144 is in the sequence because 144^2+1= 89*233.
%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==89, AppendTo[lst, n]], {n, 2, 10000}]; lst
%t p = 89; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[12000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* _Amiram Eldar_, Aug 16 2019 *)
%Y Cf. A089120,A002313,A209874,A248527-A248531,A248549-A248553.
%K nonn,easy
%O 1,1
%A _Michel Lagneau_, Oct 08 2014
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