A235934 - OEIS

%I #7 Apr 06 2014 04:10:04

%S 2,3,23,311,1777,2341,2861,3329,3833,4051,8753,9007,11587,13093,13309,

%T 14551,16001,19687,23143,26993,37309,41981,44131,45491,54623,56431,

%U 56821,57991,60223,61643,66413,66883,67511,68767,69029,70003,75743,76261,76819,80021

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

%C By the general conjecture in A235925, this sequence should have infinitely many terms.

%H Zhi-Wei Sun, <a href="/A235934/b235934.txt">Table of n, a(n) for n = 1..2000</a>

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

%e a(3) = 23 with 23, f(23) = 61, f(61) = 223 and f(223) = 1187 all prime.

%t f[n_]:=Prime[n]-n+1

%t p[k_]:=PrimeQ[f[Prime[k]]]&&PrimeQ[f[f[Prime[k]]]]&&PrimeQ[f[f[f[Prime[k]]]]]

%t n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10000}]

%Y Cf. A000040, A234694, A234695, A235924, A235925.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 17 2014