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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 02:52 EDT 2020. Contains 337950 sequences. (Running on oeis4.)