A248530 -id:A248530 - cp's OEIS frontend

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

Michel Lagneau, Oct 08 2014

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

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

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

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

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

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

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 *)

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

Original entry on oeis.org

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

Michel Lagneau, Oct 08 2014

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

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

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

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

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

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

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 *)

cp's OEIS Frontend

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

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