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Numbers n such that the smallest prime divisor of n^2+1 is 101.
5

%I #10 Oct 01 2024 15:51:22

%S 10,414,596,1000,1020,1606,1626,2030,2414,2434,2616,3444,3626,3646,

%T 4030,5040,5060,5646,5666,6070,6454,6474,6656,6676,7060,7464,7666,

%U 7686,8070,8090,8474,8696,9080,9504,10090,10494,10696,10716,11504,11706,12534,12716,12736

%N Numbers n such that the smallest prime divisor of n^2+1 is 101.

%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(13).

%C a(n)== 10 or 192 (mod 202).

%H Amiram Eldar, <a href="/A248553/b248553.txt">Table of n, a(n) for n = 1..10000</a>

%e 414 is in the sequence because 414^2+1= 101*1697.

%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==101, AppendTo[lst, n]], {n, 2, 10000}]; lst

%t 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 *)

%t Select[Range[13000],FactorInteger[#^2+1][[1,1]]==101&] (* _Harvey P. Dale_, Oct 01 2024 *)

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

%K nonn,easy

%O 1,1

%A _Michel Lagneau_, Oct 08 2014