A248531 Numbers n such that the smallest prime divisor of n^2+1 is 41.

50, 114, 196, 214, 296, 624, 706, 770, 870, 934, 1034, 1180, 1280, 1426, 1444, 1590, 1690, 1754, 1836, 1936, 2000, 2164, 2246, 2264, 2346, 2574, 2674, 2756, 2820, 2984, 3066, 3084, 3230, 3330, 3394, 3494, 3576, 3640, 3740, 3886, 3904, 4214, 4296, 4460, 4624

Offset

1,1

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(7).

a(n)== 32 or 50 (mod 82).

Links

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

Example

50 is in the sequence because 50^2+1= 41*61.

Mathematica

lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==41, AppendTo[lst, n]], {n, 2, 2000}]; lst
Select[Range[5000], FactorInteger[#^2+1][[1, 1]]==41&] (* Harvey P. Dale, Aug 15 2017 *)
p = 41; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[5000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

Prog

(Magma) [n: n in [2..5000] | PrimeDivisors(n^2+1)[1] eq 41]; // Bruno Berselli, Oct 08 2014

Crossrefs

Cf. A089120, A002313, A209874, A248527, A248528, A248529, A248530.

Sequence in context: A250724 A044237 A044618 * A222822 A212226 A031397

Adjacent sequences: A248528 A248529 A248530 * A248532 A248533 A248534

Keyword

nonn,easy

Author

Michel Lagneau, Oct 08 2014

Status

approved