OFFSET
2,3
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
R. J. Mathar, Table of n, a(n) for n = 2..3132
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. Six of these are less than 19/2. Hence a(8)=6.
MAPLE
A178151 := proc(n)
local r, a, p;
p := ithprime(n) ;
a := 0 ;
for r from 1 to p/2 do
if numtheory[legendre](r, p) =1 then
a := a+1 ;
end if;
end do:
a;
end proc: # R. J. Mathar, Feb 10 2017
MATHEMATICA
Table[p=Prime[n]; Length[Select[Range[(p-1)/2], JacobiSymbol[ #, p]==1&]], {n, 2, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 21 2010
STATUS
approved