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A248553
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Numbers n such that the smallest prime divisor of n^2+1 is 101.
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5
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10, 414, 596, 1000, 1020, 1606, 1626, 2030, 2414, 2434, 2616, 3444, 3626, 3646, 4030, 5040, 5060, 5646, 5666, 6070, 6454, 6474, 6656, 6676, 7060, 7464, 7666, 7686, 8070, 8090, 8474, 8696, 9080, 9504, 10090, 10494, 10696, 10716, 11504, 11706, 12534, 12716, 12736
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OFFSET
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1,1
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COMMENTS
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Or numbers n such that the smallest prime divisor of n^2+1 is A002313(13).
a(n)== 10 or 192 (mod 202).
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LINKS
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EXAMPLE
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414 is in the sequence because 414^2+1= 101*1697.
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MATHEMATICA
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lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==101, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 101; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[13000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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