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A240920 Prime numbers that occur as divisors of numbers of the form m^2 + 5.

%I A240920 #35 Nov 29 2016 03:27:01
%S A240920 2,3,5,7,23,29,41,43,47,61,67,83,89,101,103,107,109,127,149,163,167,
%T A240920 181,223,227,229,241,263,269,281,283,307,347,349,367,383,389,401,409,
%U A240920 421,443,449,461,463,467,487,503,509,521,523,541,547,563
%N A240920 Prime numbers that occur as divisors of numbers of the form m^2 + 5.
%C A240920 Conjecture: a prime number is in this sequence if and only if its next-to-last digit is even.
%C A240920 The law of quadratic reciprocity shows an odd prime is in the sequence if and only if it is 1, 3, 5, 7 or 9 (mod 20). This proves the above conjecture, so the sequence is the union of {2, 5} and A139513. - _Jens Kruse Andersen_, Aug 09 2014
%H A240920 Jens Kruse Andersen, <a href="/A240920/b240920.txt">Table of n, a(n) for n = 1..10000</a>
%H A240920 David Lowry-Duda, <a href="http://www.jstor.org/stable/10.4169/college.math.j.46.1.56">Unexpected Conjectures about -5 Modulo Primes</a>, College Mathematics Journal, Vol. 46, No. 1 (Jan 2015), pp.56-57.
%F A240920 a(n) ~ 2n log n. - _Charles R Greathouse IV_, Nov 29 2016
%e A240920 23 is in the sequence because it divides 8^2+5=69 with m=8.
%p A240920 isA240920 := proc(p)
%p A240920     local n;
%p A240920     if isprime(p) then
%p A240920         for n from 0 to p do
%p A240920             if modp(n^2+5,p) = 0 then
%p A240920                 return true;
%p A240920             end if;
%p A240920         end do:
%p A240920         false;
%p A240920     else
%p A240920         false;
%p A240920     end if;
%p A240920 end proc:
%p A240920 for i from 1 to 600 do
%p A240920     p := ithprime(i) ;
%p A240920     if isA240920(p) then
%p A240920         printf("%d,",p);
%p A240920     end if;
%p A240920 end do:
%o A240920 (PARI) select(p->issquare(Mod(-5,p)), primes(100)) \\ _Charles R Greathouse IV_, Nov 29 2016
%Y A240920 Cf. A002313 (k=1 or k=4), A033203 (k=2), A045331 (k=3), A139513.
%K A240920 nonn,easy
%O A240920 1,1
%A A240920 _J. Lowell_, Aug 02 2014