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A248532 Numbers n such that the smallest prime divisor of n^2+1 is 53. 1
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 (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(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
Sequence in context: A039486 A092890 A261705 * A186896 A202173 A004924
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Oct 08 2014
STATUS
approved

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Last modified March 2 21:08 EST 2024. Contains 370498 sequences. (Running on oeis4.)