A165951 a(n) = (Sum of the quadratic non-residues of prime(n) - Sum of the quadratic residues of prime(n)) / prime(n).

0, 0, 0, 1, 1, 0, 0, 1, 3, 0, 3, 0, 0, 1, 5, 0, 3, 0, 1, 7, 0, 5, 3, 0, 0, 0, 5, 3, 0, 0, 5, 5, 0, 3, 0, 7, 0, 1, 11, 0, 5, 0, 13, 0, 0, 9, 3, 7, 5, 0, 0, 15, 0, 7, 0, 13, 0, 11, 0, 0, 3, 0, 3, 19, 0, 0, 3, 0, 5, 0, 0, 19, 9, 0, 3, 17, 0, 0, 0, 0, 9, 0, 21, 0, 15, 5, 0, 0, 0, 7, 7, 25, 7, 9, 3, 21, 0, 0

Offset: 1

Author

Christopher Hunt Gribble, Oct 01 2009

Keywords

• nonn

Comments

The positive terms are A002143 minus its first term (for p=3, A002143(1)=1 corresponds to 0 here). - Javier Múgica, Nov 23 2024

Links

• C. H. Gribble, Table of n, a(n) for n=1,..., 348513 (i.e. for primes < 5x10^6).

Crossrefs

Cf. A076410, A125616.

Cf. allso A002143 (positive terms).

Formula

a(n) = Sum_{j=1..prime(n)-1} floor(j^2/prime(n)) - floor((prime(n)-2)*(prime(n)-1)/3) for n >= 3.

a(n) = A125616(n) - A076410(n) for n>=3.

Extensions

a(1)-a(2) added by Christopher Hunt Gribble, Oct 07 2009