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

1,1

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(5).

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A287767 A050961 A264445 * A204769 A333040 A250778

Adjacent sequences: A248526 A248527 A248528 * A248530 A248531 A248532

Keyword

nonn,easy

Author

Michel Lagneau, Oct 08 2014

Status

approved