A171555 - OEIS

A171555

Numbers of the form prime(n)*(prime(n)-1)/4.

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

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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

Cf. A005098, A007742, A008837.

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

Adjacent sequences: A171552 A171553 A171554 * A171556 A171557 A171558

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Dec 11 2009

EXTENSIONS

Corrected (16448 inserted, 25043 inserted) by R. J. Mathar, May 22 2010

STATUS

approved