A330304 - OEIS

%I #30 Jan 18 2020 04:39:55

%S 2,34057,36847,207997,612967,11035807,14015167,19251097,19587577,

%T 25602547,26953957,28060717,29722177,29808277,32894437,40874857,

%U 41691607,49713127,53064877,54539827,69143017,85320577,101516137,110327797,110712247,123088117,131584417,140028607,150780517

%N 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.

%C Subsequence of A005382.

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

%C 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).

%H Chai Wah Wu, <a href="/A330304/b330304.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%o (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

%Y Cf. A005382.

%K nonn

%O 1,1

%A _Pierre CAMI_, Dec 13 2019

%E a(12) and a(15) corrected by _Chai Wah Wu_, Jan 17 2020