%I #12 Sep 08 2022 08:46:10

%S 4,30,64,106,140,166,234,276,310,336,344,370,404,446,480,506,514,540,

%T 574,650,676,744,786,820,846,854,880,914,956,990,1016,1024,1050,1160,

%U 1186,1194,1220,1254,1296,1330,1356,1364,1390,1424,1466,1534,1560,1636,1670

%N Numbers n such that the smallest prime divisor of n^2+1 is 17.

%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(4).

%C a(n)== 4 or 30 (mod 34).

%H Amiram Eldar, <a href="/A248528/b248528.txt">Table of n, a(n) for n = 1..10000</a>

%e 30 is in the sequence because 30^2+1= 17*53.

%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==17, AppendTo[lst, n]], {n, 2, 2000}]; lst

%t p = 17; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[1670], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* _Amiram Eldar_, Aug 16 2019 *)

%o (Magma) [n: n in [2..2000] | PrimeDivisors(n^2+1)[1] eq 17]; // _Bruno Berselli_, Oct 08 2014

%Y Cf. A089120, A002313, A248527.

%K nonn,easy

%O 1,1

%A _Michel Lagneau_, Oct 08 2014