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A171555 Numbers of the form prime(n)*(prime(n)-1)/4. 7
5, 39, 68, 203, 333, 410, 689, 915, 1314, 1958, 2328, 2525, 2943, 3164, 4658, 5513, 6123, 7439, 8145, 9264, 9653, 13053, 13514, 14460, 16448, 18023, 19113, 19670, 21389, 24414, 25043, 28308, 30363, 31064, 34689, 37733, 39303, 40100, 41718, 44205, 46764, 50288 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The halfs of even numbers of 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
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
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: A299054 A095230 A247708 * A153267 A183477 A219086
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected (16448 inserted, 25043 inserted) by R. J. Mathar, May 22 2010
STATUS
approved

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Last modified June 13 03:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)