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%I #8 Aug 16 2019 15:12:11
%S 194,316,416,804,904,926,1026,1170,1270,1414,1536,1780,2024,2490,2734,
%T 2856,3000,3100,3244,3344,3366,3610,3954,3976,4320,4564,4830,4930,
%U 5074,5196,5540,5684,6394,6416,6516,6760,6904,7004,7126,7270,7370,7514,7614,7736
%N Numbers n such that the smallest prime divisor of n^2+1 is 61.
%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(9).
%C a(n)== 50 or 72 (mod 122).
%H Amiram Eldar, <a href="/A248549/b248549.txt">Table of n, a(n) for n = 1..10000</a>
%e 194 is in the sequence because 194^2+1= 61*617.
%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==61, AppendTo[lst, n]], {n, 2, 10000}]; lst
%t p = 61; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[8000], 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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