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%I #22 Dec 24 2022 13:47:18
%S 5,39,68,203,333,410,689,915,1314,1958,2328,2525,2943,3164,4658,5513,
%T 6123,7439,8145,9264,9653,13053,13514,14460,16448,18023,19113,19670,
%U 21389,24414,25043,28308,30363,31064,34689,37733,39303,40100,41718,44205,46764,50288
%N Numbers of the form prime(n)*(prime(n)-1)/4.
%C The halfs of even numbers of p(p-1)/2 for p prime.
%C 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
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.21 p. 110.
%H Alois P. Heinz, <a href="/A171555/b171555.txt">Table of n, a(n) for n = 1..10000</a>
%H Aebi, Christian, and Grant Cairns. <a href="http://arxiv.org/abs/1512.00896">Sums of Quadratic residues and nonresidues</a>, arXiv preprint arXiv:1512.00896 (2015).
%t Table[Table[Mod[a^2, p], {a, 1, (p - 1)/2}] // Total, {p,
%t Select[Prime[Range[100]], Mod[#, 4] == 1 &]}] (* _Geoffrey Critzer_, May 07 2015 *)
%t Select[(# (#-1))/4&/@Prime[Range[100]],IntegerQ] (* _Harvey P. Dale_, Dec 24 2022 *)
%o (PARI) lista(nn) = forprime(p=2, nn, if ((p % 4)==1, print1(p*(p-1)/4, ", "))); \\ _Michel Marcus_, Mar 23 2016
%Y Cf. A005098, A007742, A008837.
%Y 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.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Dec 11 2009
%E Corrected (16448 inserted, 25043 inserted) by _R. J. Mathar_, May 22 2010
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