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A230217 List of those primes p with p + 6 and 3*p + 8 also prime. 6

%I

%S 5,7,11,13,17,31,41,47,53,61,73,83,101,103,131,151,157,167,193,223,

%T 251,263,271,277,307,311,347,367,433,563,571,593,601,613,641,647,677,

%U 733,823,857,977,1097,1117,1217,1223,1231,1291,1301,1361,1427

%N List of those primes p with p + 6 and 3*p + 8 also prime.

%C Clearly, no term is congruent to 4 modulo 5.

%C This sequence is interesting because of the conjecture in the comments in A230219.

%H Zhi-Wei Sun, <a href="/A230217/b230217.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 5 since neither 2 + 6 nor 3 + 6 is prime, but 5 + 6 = 11 and 3*5 + 8 = 23 are both prime.

%t PQ[p_]:=PrimeQ[p+6]&&PrimeQ[3p+8]

%t m=0

%t Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,225}]

%Y Cf. A023201, A230219.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Oct 11 2013

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Last modified November 27 00:20 EST 2022. Contains 358362 sequences. (Running on oeis4.)