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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 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

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