A178152 The number of quadratic residues (mod p) greater than p/2, where p=prime(n).

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

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 half-interval

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, p-1], JacobiSymbol[ #, p]==1&]], {n, 2, 100}]

Crossrefs

Cf. A178151, A178153, A178154

Sequence in context: A061988 A094151 A135800 * A006984 A361458 A087275

Adjacent sequences: A178149 A178150 A178151 * A178153 A178154 A178155

Keyword

nonn

Author

T. D. Noe, May 21 2010

Status

approved