|
| |
|
|
A125616
|
|
(Sum of the quadratic nonresidues of prime(n)) / prime(n).
|
|
2
|
|
|
|
1, 2, 3, 3, 4, 5, 7, 7, 9, 9, 10, 11, 14, 13, 16, 15, 17, 21, 18, 22, 22, 22, 24, 25, 28, 28, 27, 28, 34, 35, 34, 36, 37, 41, 39, 41, 47, 43, 47, 45, 54, 48, 49, 54, 54, 59, 59, 57, 58, 67, 60, 66, 64, 72, 67, 73, 69, 70, 72, 73, 78, 87, 78, 79, 84, 84, 89, 87, 88, 99, 96, 93, 96
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,2
|
|
|
COMMENTS
|
Always an integer for primes >= 5.
|
|
|
REFERENCES
|
D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.
|
|
|
LINKS
|
N. Hobson, Table of n, a(n) for n = 3..1000
N. Hobson, Home page (listed in lieu of email address)
|
|
|
FORMULA
|
a(n) = A125615(n)/prime(n).
If prime(n) = 4k+1 then a(n) = k = A076410(n).
|
|
|
EXAMPLE
|
The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = (3+5+6)/7 = 2.
|
|
|
MAPLE
|
a:= proc(n) local p;
p:= ithprime(n);
convert(select(t->numtheory:-legendre(t, p)=-1, [$1..p-1]), `+`)/p;
end proc:
seq(a(n), n=3..100); # Robert Israel, May 10 2015
|
|
|
MATHEMATICA
|
Table[Total[Flatten[Position[Table[JacobiSymbol[a, p], {a, p - 1}], -1]]]/ p, {p, Prime[Range[3, 100]]}] (* Geoffrey Critzer, May 10 2015 *)
|
|
|
PROG
|
(PARI) vector(73, m, p=prime(m+2); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)); (p-1)/2-t/p)
|
|
|
CROSSREFS
|
Cf. A002143, A076409, A076410, A125613-A125618.
Sequence in context: A304885 A017853 A241518 * A141472 A029034 A343941
Adjacent sequences: A125613 A125614 A125615 * A125617 A125618 A125619
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Nick Hobson, Nov 30 2006
|
|
|
STATUS
|
approved
|
| |
|
|
