A248530 Numbers n such that the smallest prime divisor of n^2+1 is 37.

6, 80, 154, 290, 364, 376, 524, 586, 660, 734, 894, 1030, 1104, 1116, 1190, 1326, 1400, 1486, 1634, 1770, 1856, 1930, 2004, 2066, 2226, 2300, 2510, 2584, 2596, 2744, 2806, 2880, 2966, 3040, 3114, 3176, 3250, 3324, 3484, 3546, 3620, 3694, 3706, 3780, 3854, 3916

Offset

1,1

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(6).

a(n)== 6 or 68 (mod 74).

Links

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

Example

80 is in the sequence because 80^2+1= 37*173.

Mathematica

lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==37, AppendTo[lst, n]], {n, 2, 4000}]; lst
p = 37; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[4000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

Prog

(Magma) [n: n in [2..4000] | PrimeDivisors(n^2+1)[1] eq 37]; // Bruno Berselli, Oct 08 2014

Crossrefs

Cf. A089120, A002313, A209874, A248527, A248528, A248529.

Sequence in context: A131237 A024082 A132547 * A229574 A240409 A275137

Adjacent sequences: A248527 A248528 A248529 * A248531 A248532 A248533

Keyword

nonn,easy

Author

Michel Lagneau, Oct 08 2014

Status

approved