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%I #10 Aug 16 2019 15:57:38
%S 366,410,604,754,1336,1530,1574,2156,2500,2544,2694,3126,3276,3470,
%T 3514,3664,4096,4290,4440,5066,5454,5604,6186,6230,6380,6424,6574,
%U 7156,8126,8170,8320,9140,9334,9484,9916,10066,10110,10260,10454,11036,11230,11424,11856
%N Numbers n such that the smallest prime divisor of n^2+1 is 97.
%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(12).
%C a(n)== 22 or 172 (mod 194).
%H Amiram Eldar, <a href="/A248552/b248552.txt">Table of n, a(n) for n = 1..10000</a>
%e 366 is in the sequence because 366^2+1= 97*1381.
%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==97, AppendTo[lst, n]], {n, 2, 10000}]; lst
%t Select[Range[12000],FactorInteger[#^2+1][[1,1]]==97&] (* _Harvey P. Dale_, Aug 11 2017 *)
%t p = 97; 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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