

A186708


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


1



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
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OFFSET

1,2


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].


LINKS

Table of n, a(n) for n=1..57.


FORMULA

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


PROG

(PARI) forprime( p=1, 499, p%4==3next; u=3; c=[1, 0]; for(i=2, p2, bittest(u, i^2%p) & next; u+=1<<(i^2%p); c[i^2%p*2\p+1]++); print1(c[1]", "))


CROSSREFS

Cf. A002145, A104635, A186709, A178154.
Sequence in context: A282896 A141437 A219645 * A227697 A097457 A321612
Adjacent sequences: A186705 A186706 A186707 * A186709 A186710 A186711


KEYWORD

nonn


AUTHOR

M. F. Hasler, Feb 25 2011


STATUS

approved



