A248529 Numbers n such that the smallest prime divisor of n^2+1 is 29.

46, 104, 186, 220, 244, 360, 394, 510, 534, 626, 766, 800, 916, 940, 974, 1056, 1090, 1114, 1206, 1264, 1346, 1380, 1404, 1496, 1520, 1554, 1694, 1810, 1844, 1926, 1960, 2076, 2100, 2134, 2216, 2250, 2366, 2390, 2424, 2506, 2564, 2680, 2714, 2796, 2830, 2854

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(5).

a(n)== 12 or 46 (mod 58).

Examples

			46 is in the sequence because 46^2+1= 29*73.
		

Links

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

Crossrefs

Cf. A089120, A002313, A209874, A248527, A248528.

Programs

Magma

[n: n in [2..3000] | PrimeDivisors(n^2+1)[1] eq 29]; // Bruno Berselli, Oct 08 2014

Mathematica

lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==29, AppendTo[lst, n]], {n, 2, 2000}]; lst
p = 29; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[3000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
Select[Range[2,3000,2],FactorInteger[#^2+1][[1,1]]==29&] (* or *) Select[ Flatten[ #+{12,46}&/@(58*Range[0,60])],FactorInteger[#^2+1][[1,1]]==29&](* Harvey P. Dale, Jul 01 2022 *)