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 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

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Last modified March 31 18:36 EDT 2023. Contains 361672 sequences. (Running on oeis4.)