A248528 Numbers n such that the smallest prime divisor of n^2+1 is 17.

4, 30, 64, 106, 140, 166, 234, 276, 310, 336, 344, 370, 404, 446, 480, 506, 514, 540, 574, 650, 676, 744, 786, 820, 846, 854, 880, 914, 956, 990, 1016, 1024, 1050, 1160, 1186, 1194, 1220, 1254, 1296, 1330, 1356, 1364, 1390, 1424, 1466, 1534, 1560, 1636, 1670

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(4).

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

Examples

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

Links

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

Crossrefs

Cf. A089120, A002313, A248527.

Programs

Magma

[n: n in [2..2000] | PrimeDivisors(n^2+1)[1] eq 17]; // Bruno Berselli, Oct 08 2014

Mathematica

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