A248552 - OEIS

%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