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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 (list; graph; refs; listen; history; text; internal format)
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

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

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 *)

CROSSREFS

Cf. A089120,A002313,A209874,A248527-A248531,A248549-A248553.

Sequence in context: A232892 A034285 A211469 * A178972 A250787 A188246

Adjacent sequences:  A248548 A248549 A248550 * A248552 A248553 A248554

KEYWORD

nonn,easy

AUTHOR

Michel Lagneau, Oct 08 2014

STATUS

approved

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Last modified August 15 07:14 EDT 2022. Contains 356128 sequences. (Running on oeis4.)