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%I #15 Sep 08 2022 08:46:10
%S 76,136,454,500,560,666,924,984,1196,1454,1514,1666,1726,2090,2196,
%T 2256,2620,2726,2786,3044,3104,3150,3210,3256,3316,3680,3786,4104,
%U 4210,4270,4316,4634,4694,4800,4846,5224,5330,5694,5800,5860,5906,5966,6224,6330,6390
%N Numbers n such that the smallest prime divisor of n^2+1 is 53.
%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(8).
%C a(n)== 30 or 76 (mod 106).
%H Amiram Eldar, <a href="/A248532/b248532.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e 76 is in the sequence because 76^2+1= 53*109.
%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==53, AppendTo[lst, n]], {n, 2, 2000}]; lst
%t Select[Range[7000],FactorInteger[#^2+1][[1,1]]==53&] (* _Harvey P. Dale_, Aug 04 2016 *)
%t p = 53; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[7000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* _Amiram Eldar_, Aug 16 2019 *)
%o (Magma) [n: n in [2..7000] | PrimeDivisors(n^2+1)[1] eq 53]; // _Bruno Berselli_, Oct 08 2014
%Y Cf. A089120, A002313, A209874, A248527, A248528, A248529, A248530, A248531.
%K nonn,easy
%O 1,1
%A _Michel Lagneau_, Oct 08 2014
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