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.
%I A186708 #10 Jul 14 2012 11:32:34 %S A186708 1,2,4,6,7,9,12,14,19,18,21,22,25,28,31,34,40,39,41,42,47,52,54,54,57, %T A186708 59,64,67,73,72,73,75,81,87,87,94,99,96,99,104,118,118,117,118,119, %U A186708 127,132,125,136,129,136,138,141,154,150,157,162 %N A186708 Number of quadratic residues (mod p) in the interval [1,2k+1], for primes p=4k+3. %C A186708 For primes of the form p=4k+3 (A002145), count numbers in [1,2k+1] which are quadratic residues mod p. %C A186708 R. K. Guy asks whether there is an elementary proof for the fact that there are always less quadratic residues in the interval [2k+2,4k+2] than in [1,2k+1]. %F A186708 a(n) = A104635(n) - A186709(n) = A186709(n) + A178154(n) = (A104635(n) + A178154(n))/2 = (A002145(n) + 2*A178154(n) - 1)/4. %o A186708 (PARI) forprime( p=1,499, p%4==3|next; u=3; c=[1,0]; for(i=2,p-2, bittest(u,i^2%p) & next; u+=1<<(i^2%p); c[i^2%p*2\p+1]++); print1(c[1]", ")) %Y A186708 Cf. A002145, A104635, A186709, A178154. %K A186708 nonn %O A186708 1,2 %A A186708 _M. F. Hasler_, Feb 25 2011