Conjecture: consecutive elements of this sequence are consecutive primes satisfying the congruence b(k) == 1 (mod k) for k>0, where b(k) is recursive sequence defined as follows: b(k) = -b(k-1) - b(k-2) + b(k-3) - b(k-4) with b(0)=2, b(1)=1, b(2)=0, b(3)=-1.
(b(59) - 1) mod 59 = (-496870918 - 1) mod 59 = 0, 59 = a(1).
(b(71) - 1) mod 71 = (88081764473 - 1) mod 71 = 0, 71 = a(2).
For 10^6 consecutive positive integers there are 9748 prime solutions and 5 nonprime (1, 586, 2935, 17161, 429737) solutions of the congruence. (End)
REFERENCES
David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.
