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A248551
Numbers n such that the smallest prime divisor of n^2+1 is 89.
1
144, 390, 856, 1746, 1814, 1924, 2170, 2526, 2636, 2704, 2814, 3170, 3416, 3594, 3704, 3950, 4060, 4306, 4840, 4950, 5306, 5484, 6374, 6620, 6730, 7086, 7154, 7264, 7866, 7976, 8044, 8154, 8400, 8756, 8866, 9044, 9400, 9646, 9824, 10180, 10290, 11070, 11426
OFFSET
1,1
COMMENTS
Or numbers n such that the smallest prime divisor of n^2+1 is A002313(11).
a(n)== 34 or 144 (mod 178).
LINKS
EXAMPLE
144 is in the sequence because 144^2+1= 89*233.
MATHEMATICA
lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==89, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 89; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[12000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Oct 08 2014
STATUS
approved