cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A248550 Numbers n such that the smallest prime divisor of n^2+1 is 73.

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%I A248550 #19 Aug 16 2019 15:23:46
%S A248550 100,246,484,630,776,830,976,1506,1706,1944,2144,2236,2290,2874,3020,
%T A248550 3604,3696,3750,3896,4134,4426,4626,4864,5064,5210,5356,5594,5740,
%U A248550 5794,5940,6086,6324,6470,6616,6670,6816,7200,7254,7346,7400,7546,7930,7984,8076
%N A248550 Numbers n such that the smallest prime divisor of n^2+1 is 73.
%C A248550 Or numbers n such that the smallest prime divisor of n^2+1 is A002313(10).
%C A248550 a(n) == 46 or 100 (mod 146).
%C A248550 No need to completely factorize n^2+1. - _David A. Corneth_, Apr 29 2017
%H A248550 Amiram Eldar, <a href="/A248550/b248550.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e A248550 100 is in the sequence because 100^2+1= 73*137.
%e A248550 246 is in the sequence because 246^2+1 isn't divisible by any prime less than 73 and is divisible by 73. - _David A. Corneth_, Apr 29 2017
%t A248550 lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==73, AppendTo[lst, n]], {n, 2, 10000}]; lst
%t A248550 Select[Range[8100],FactorInteger[#^2+1][[1,1]]==73&] (* _Harvey P. Dale_, Apr 29 2017 *)
%t A248550 p = 73; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[8000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* _Amiram Eldar_, Aug 16 2019 *)
%o A248550 (PARI) is(n) = {my(m=n%146, p=2, n21 = n^2+1, v=[5, 13, 17, 29, 37, 41, 53, 61]);
%o A248550 return(abs(73-m)==27&&sum(i=1, #v, p=nextprime(p+1); valuation(n21,v[i]))==0)}
%o A248550 upto(n) = {my(l=List(), i=54, m=46); while(m<n, if(is(m), listput(l, m)); m+=i; i=146-i); l} \\ _David A. Corneth_, Apr 29 2017
%Y A248550 Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.
%K A248550 nonn,easy
%O A248550 1,1
%A A248550 _Michel Lagneau_, Oct 08 2014