A248532 Numbers n such that the smallest prime divisor of n^2+1 is 53.

76, 136, 454, 500, 560, 666, 924, 984, 1196, 1454, 1514, 1666, 1726, 2090, 2196, 2256, 2620, 2726, 2786, 3044, 3104, 3150, 3210, 3256, 3316, 3680, 3786, 4104, 4210, 4270, 4316, 4634, 4694, 4800, 4846, 5224, 5330, 5694, 5800, 5860, 5906, 5966, 6224, 6330, 6390

Offset

1,1

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(8).

a(n)== 30 or 76 (mod 106).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

76 is in the sequence because 76^2+1= 53*109.

Mathematica

lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==53, AppendTo[lst, n]], {n, 2, 2000}]; lst
Select[Range[7000], FactorInteger[#^2+1][[1, 1]]==53&] (* Harvey P. Dale, Aug 04 2016 *)
p = 53; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[7000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

Prog

(Magma) [n: n in [2..7000] | PrimeDivisors(n^2+1)[1] eq 53]; // Bruno Berselli, Oct 08 2014

Crossrefs

Cf. A089120, A002313, A209874, A248527, A248528, A248529, A248530, A248531.

Sequence in context: A039486 A092890 A261705 * A186896 A202173 A004924

Adjacent sequences: A248529 A248530 A248531 * A248533 A248534 A248535

Keyword

nonn,easy

Author

Michel Lagneau, Oct 08 2014

Status

approved