A248553 Numbers n such that the smallest prime divisor of n^2+1 is 101.

10, 414, 596, 1000, 1020, 1606, 1626, 2030, 2414, 2434, 2616, 3444, 3626, 3646, 4030, 5040, 5060, 5646, 5666, 6070, 6454, 6474, 6656, 6676, 7060, 7464, 7666, 7686, 8070, 8090, 8474, 8696, 9080, 9504, 10090, 10494, 10696, 10716, 11504, 11706, 12534, 12716, 12736

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(13).

a(n)== 10 or 192 (mod 202).

Examples

			414 is in the sequence because 414^2+1= 101*1697.
		

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]]==101, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 101; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[13000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
Select[Range[13000],FactorInteger[#^2+1][[1,1]]==101&] (* Harvey P. Dale, Oct 01 2024 *)