A248552 Numbers n such that the smallest prime divisor of n^2+1 is 97.

366, 410, 604, 754, 1336, 1530, 1574, 2156, 2500, 2544, 2694, 3126, 3276, 3470, 3514, 3664, 4096, 4290, 4440, 5066, 5454, 5604, 6186, 6230, 6380, 6424, 6574, 7156, 8126, 8170, 8320, 9140, 9334, 9484, 9916, 10066, 10110, 10260, 10454, 11036, 11230, 11424, 11856

Offset: 1

Author

Michel Lagneau, Oct 08 2014

Keywords

• nonn
• easy

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(12).

a(n)== 22 or 172 (mod 194).

Examples

			366 is in the sequence because 366^2+1= 97*1381.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.

Programs

Mathematica

lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==97, AppendTo[lst, n]], {n, 2, 10000}]; lst
Select[Range[12000],FactorInteger[#^2+1][[1,1]]==97&] (* Harvey P. Dale, Aug 11 2017 *)
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 *)