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Consider pairs of primes p<q such that p|q^2 + q + 1 and q|p^2 + p + 1; sequence gives q values.
1

%I #11 Apr 13 2020 05:40:33

%S 13,61,107419560853453

%N Consider pairs of primes p<q such that p|q^2 + q + 1 and q|p^2 + p + 1; sequence gives q values.

%H T. Cai, Z. Shen, L. Jia, <a href="http://arxiv.org/abs/1503.02798">A congruence involving harmonic sums modulo p^alpha q^beta</a>, arXiv preprint arXiv:1503.02798 [math.NT], 2015.

%H Yong-Gao Chen, and Xin Tong, <a href="https://doi.org/10.1016/j.jnt.2015.02.004">On a conjecture of de Koninck</a>, Journal of Number Theory, Volume 154, September 2015, Pages 324-364. See Remark 2 p. 331.

%e The known pairs are (3, 13),(13, 61),(22419767768701, 107419560853453).

%Y Cf. A264611.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Nov 25 2015