OFFSET
1,1
COMMENTS
The halves of even numbers of the form p(p-1)/2 for p prime.
Sum of the quadratic residues of primes of the form 4k + 1. For example, a(3)=68 because 17 is the 3rd prime of the form 4k + 1 and the quadratic residues of 17 are 1, 4, 9, 16, 8, 2, 15, 13 which sum to 68. This sum is also the sum of the quadratic nonresidues. Cf. A230077. - Geoffrey Critzer, May 07 2015
REFERENCES
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.21 p. 110.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).
MATHEMATICA
Table[Table[Mod[a^2, p], {a, 1, (p - 1)/2}] // Total, {p,
Select[Prime[Range[100]], Mod[#, 4] == 1 &]}] (* Geoffrey Critzer, May 07 2015 *)
Select[(# (#-1))/4&/@Prime[Range[100]], IntegerQ] (* Harvey P. Dale, Dec 24 2022 *)
PROG
(PARI) lista(nn) = forprime(p=2, nn, if ((p % 4)==1, print1(p*(p-1)/4, ", "))); \\ Michel Marcus, Mar 23 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Dec 11 2009
EXTENSIONS
Corrected (16448 inserted, 25043 inserted) by R. J. Mathar, May 22 2010
STATUS
approved