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

Author

Pierre CAMI, Dec 13 2019

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

Cf. A005382.

Programs

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

Extensions

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