login
A125615
Sum of the quadratic nonresidues of prime(n).
11
0, 2, 5, 14, 33, 39, 68, 95, 161, 203, 279, 333, 410, 473, 658, 689, 944, 915, 1139, 1491, 1314, 1738, 1826, 1958, 2328, 2525, 2884, 2996, 2943, 3164, 4318, 4585, 4658, 5004, 5513, 6191, 6123, 6683, 7849, 7439, 8413, 8145, 10314, 9264, 9653, 10746, 11394
OFFSET
1,2
COMMENTS
For all n > 2, prime(n) divides a(n).
REFERENCES
D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.
LINKS
Christian Aebi and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 [math.NT], 2015.
FORMULA
If prime(n) = 4k+1 then a(n) = k(4k+1) = A076409(n).
EXAMPLE
The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4) = 3+5+6 = 14.
PROG
(PARI) vector(47, n, p=prime(n); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)); p*(p-1)/2-t)
CROSSREFS
Sums of residues, nonresidues, and their differences, for p == 1 (mod 4), p == 3 (mod 4), and all p: A171555; A282035, A282036, A282037; A076409, A125615, A282038.
Sequence in context: A336229 A296502 A036681 * A096772 A090803 A018015
KEYWORD
easy,nonn
AUTHOR
Nick Hobson, Nov 30 2006
STATUS
approved