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A235934 Primes p with f(p), f(f(p)) and f(f(f(p))) all prime, where f(n) = prime(n) - n + 1.

%I A235934 #7 Apr 06 2014 04:10:04
%S A235934 2,3,23,311,1777,2341,2861,3329,3833,4051,8753,9007,11587,13093,13309,
%T A235934 14551,16001,19687,23143,26993,37309,41981,44131,45491,54623,56431,
%U A235934 56821,57991,60223,61643,66413,66883,67511,68767,69029,70003,75743,76261,76819,80021
%N A235934 Primes p with f(p), f(f(p)) and f(f(f(p))) all prime, where f(n) = prime(n) - n + 1.
%C A235934 By the general conjecture in A235925, this sequence should have infinitely many terms.
%H A235934 Zhi-Wei Sun, <a href="/A235934/b235934.txt">Table of n, a(n) for n = 1..2000</a>
%H A235934 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A235934 a(3) = 23 with 23, f(23) = 61, f(61) = 223 and f(223) = 1187 all prime.
%t A235934 f[n_]:=Prime[n]-n+1
%t A235934 p[k_]:=PrimeQ[f[Prime[k]]]&&PrimeQ[f[f[Prime[k]]]]&&PrimeQ[f[f[f[Prime[k]]]]]
%t A235934 n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10000}]
%Y A235934 Cf. A000040, A234694, A234695, A235924, A235925.
%K A235934 nonn
%O A235934 1,1
%A A235934 _Zhi-Wei Sun_, Jan 17 2014