

A178151


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


3



1, 1, 2, 4, 3, 4, 6, 7, 7, 9, 9, 10, 12, 14, 13, 19, 15, 18, 21, 18, 22, 25, 22, 24, 25, 28, 31, 27, 28, 34, 40, 34, 39, 37, 41, 39, 42, 47, 43, 52, 45, 54, 48, 49, 54, 57, 59, 64, 57, 58, 67, 60, 73, 64, 72, 67, 73, 69, 70, 75, 73, 81, 87, 78, 79, 87, 84, 94, 87, 88, 99, 96, 93
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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 halfinterval


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[(p1)/2], JacobiSymbol[ #, p]==1&]], {n, 2, 100}]


CROSSREFS

Cf. A178152, A178153, A178154
Sequence in context: A224714 A089169 A291563 * A087794 A050514 A229047
Adjacent sequences: A178148 A178149 A178150 * A178152 A178153 A178154


KEYWORD

nonn


AUTHOR

T. D. Noe, May 21 2010


STATUS

approved



