A248549 Numbers n such that the smallest prime divisor of n^2+1 is 61.

194, 316, 416, 804, 904, 926, 1026, 1170, 1270, 1414, 1536, 1780, 2024, 2490, 2734, 2856, 3000, 3100, 3244, 3344, 3366, 3610, 3954, 3976, 4320, 4564, 4830, 4930, 5074, 5196, 5540, 5684, 6394, 6416, 6516, 6760, 6904, 7004, 7126, 7270, 7370, 7514, 7614, 7736

Offset

1,1

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(9).

a(n)== 50 or 72 (mod 122).

Links

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

Example

194 is in the sequence because 194^2+1= 61*617.

Mathematica

lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==61, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 61; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[8000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

Crossrefs

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

Sequence in context: A025325 A294578 A294595 * A278123 A158224 A205621

Adjacent sequences: A248546 A248547 A248548 * A248550 A248551 A248552

Keyword

nonn,easy

Author

Michel Lagneau, Oct 08 2014

Status

approved