login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 21:28 EST 2022. Contains 358698 sequences. (Running on oeis4.)