A330304 Prime numbers P such that Q=2*P-1, R=4*Q+1, S=6*R+1, T=8*S-1, U=10*T+1 and V=12*U-1 are all prime numbers.

2, 34057, 36847, 207997, 612967, 11035807, 14015167, 19251097, 19587577, 25602547, 26953957, 28060717, 29722177, 29808277, 32894437, 40874857, 41691607, 49713127, 53064877, 54539827, 69143017, 85320577, 101516137, 110327797, 110712247, 123088117, 131584417, 140028607, 150780517

Offset

1,1

Comments

Subsequence of A005382.

a(1) = A005382(1), a(2) = A005382(505), a(3) = A005382(536), a(4) = A005382(2084), a(5) = A005382(5105); a(6) > A005382(10000).

P, Q, R, S, T, U, V are 7 primes in near-geometric progression (2, 4, 6, 8, 10, 12 plus or minus one) starting P = a(n).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Example

2*2-1=3, 4*3+1=13, 6*13+1=79, 8*79-1=631, 10*631+1=6311, 12*6311-1=75731, where 2, 3, 13, 79, 631, 6311 and 75731 are all prime numbers; so 2 is the first term.

Prog

(PARI) forprime(P=2, 130000000, my(Q=2*P-1, R=4*Q+1, S=6*R+1, T=8*S-1, U=10*T+1, V=12*U-1); if(isprime(Q)&&isprime(R)&&isprime(S)&&isprime(T)&&isprime(U)&&isprime(V), print1(P, ", "))) \\ Hugo Pfoertner, Dec 17 2019

Crossrefs

Cf. A005382.

Sequence in context: A228556 A001377 A206854 * A272166 A291881 A257968

Adjacent sequences: A330301 A330302 A330303 * A330305 A330306 A330307

Keyword

nonn

Author

Pierre CAMI, Dec 13 2019

Extensions

a(12) and a(15) corrected by Chai Wah Wu, Jan 17 2020

Status

approved