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 A218825 Number of ways to write 2n-1 as p+2q with p, q and p^2+60q^2 all prime. 10
 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 3, 1, 3, 3, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 2, 2, 1, 3, 1, 1, 3, 3, 4, 3, 1, 2, 5, 3, 1, 3, 2, 4, 3, 3, 1, 7, 4, 1, 5, 3, 5, 8, 4, 3, 4, 3, 3, 5, 4, 4, 3, 2, 3, 5, 3, 5, 7, 3, 2, 9, 4, 4, 6, 3, 3, 8, 6, 1, 4, 5, 2, 7, 1, 4, 2, 4, 5, 5, 2, 4, 4, 3, 2, 5, 4, 5, 6, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS Conjecture: a(n)>0 for all n>8. This conjecture is stronger than Lemoine's conjecture. It has been verified for n up to 10^8. Zhi-Wei Sun also made the following general conjecture: For any positive integer n, the set E(n) of positive odd integers not of the form p+2q with p, q, p^2+4(2^n-1)q^2 all prime, is finite. In particular, if we let M(n) denote the maximal element of E(n), then M(1)=3449, M(2)=1711, E(3)={1,3,5,7,31,73}, E(4)={1,3,5,7,9,11,13,15},   M(5)=6227, M(6)=1051, M(7)=2239, M(8)=2599, M(9)=7723,   M(10)=781, M(11)=1163, M(12)=587, M(13)=11443,   M(14)=2279, M(15)=157, M(16)=587, M(17)=32041,   M(18)=1051, M(19)=2083, M(20)=4681. Zhi-Wei Sun also guessed that for any positive even integer d not congruent to 2 modulo 6 there exists a prime p(d) such that for any prime p>p(d) there is a prime q

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)