A238776 - OEIS

%I #10 Mar 05 2014 08:28:24

%S 2,5,7,13,31,41,43,83,109,151,211,281,307,317,349,353,499,601,709,757,

%T 883,911,971,1447,1453,1483,1531,1801,2053,2281,2819,2833,3163,3329,

%U 3331,3881,3907,4051,4243,4447,4451,4703,4751,5483,5659,5701,5737,6011,6271,6311,6361,6379,6427,6571,6827,6841,6983,7159,7879,8209

%N Primes p with prime(p) - p + 1 and prime(q) - q + 1 both prime, where q = prime(2*pi(p)+1) with pi(.) given by A000720.

%C Conjecture: The sequence has infinitely many terms.

%C This is motivated by the conjecture in A238766. Note that the sequence is a subsequence of A234695.

%H Zhi-Wei Sun, <a href="/A238776/b238776.txt">Table of n, a(n) for n = 1..10000</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014.

%e a(1) = 2 since prime(2) - 2 + 1 = 2 and prime(prime(2*pi(2)+1)) - prime(2*pi(2)+1) + 1 = prime(5) - 5 + 1 = 11 - 4 = 7 are both prime.

%t p[k_]:=PrimeQ[Prime[Prime[k]]-Prime[k]+1]

%t n=0;Do[If[p[k]&&p[2k+1],n=n+1;Print[n," ",Prime[k]]],{k,1,1029}]

%Y Cf. A000040, A000720, A234695, A238766.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Mar 05 2014