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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.

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A186708 Number of quadratic residues (mod p) in the interval [1,2k+1], for primes p=4k+3.

Original entry on oeis.org

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, 59, 64, 67, 73, 72, 73, 75, 81, 87, 87, 94, 99, 96, 99, 104, 118, 118, 117, 118, 119, 127, 132, 125, 136, 129, 136, 138, 141, 154, 150, 157, 162
Offset: 1

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Author

M. F. Hasler, Feb 25 2011

Keywords

Comments

For primes of the form p=4k+3 (A002145), count numbers in [1,2k+1] which are quadratic residues mod p.
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].

Crossrefs

Cf. A002145, A104635, A186709, A178154.

Programs

  • 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]", "))

Formula

a(n) = A104635(n) - A186709(n) = A186709(n) + A178154(n) = (A104635(n) + A178154(n))/2 = (A002145(n) + 2*A178154(n) - 1)/4.
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