

A178152


The number of quadratic residues (mod p) greater than p/2, where p=prime(n).


2



0, 1, 1, 1, 3, 4, 3, 4, 7, 6, 9, 10, 9, 9, 13, 10, 15, 15, 14, 18, 17, 16, 22, 24, 25, 23, 22, 27, 28, 29, 25, 34, 30, 37, 34, 39, 39, 36, 43, 37, 45, 41, 48, 49, 45, 48, 52, 49, 57, 58, 52, 60, 52, 64, 59, 67, 62, 69, 70, 66, 73, 72, 68, 78, 79, 78, 84, 79, 87, 88, 80, 87, 93, 90
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,5


COMMENTS

Sequence A063987 lists the quadratic residues (mod p) for each prime p. When p=1 (mod 4), there are an equal number of quadratic residues less than p/2 and greater than p/2. When p=3 (mod 4), there are always more quadratic residues less than p/2 than greater than p/2.


LINKS

Table of n, a(n) for n=2..75.
MathOverflow, Most squares in the first halfinterval


EXAMPLE

The quadratic residues of 19, the 8th prime, are 1, 4, 5, 6, 7, 9, 11, 16, 17. Three of these are greater than 19/2. Hence a(8)=3.


MATHEMATICA

Table[p=Prime[n]; Length[Select[Range[(p+1)/2, p1], JacobiSymbol[ #, p]==1&]], {n, 2, 100}]


CROSSREFS

Cf. A178151, A178153, A178154
Sequence in context: A061988 A094151 A135800 * A006984 A087275 A265305
Adjacent sequences: A178149 A178150 A178151 * A178153 A178154 A178155


KEYWORD

nonn


AUTHOR

T. D. Noe, May 21 2010


STATUS

approved



