A235984 - OEIS

%I #7 Apr 06 2014 04:11:25

%S 2,3,501187,560029,2076881,2836003,2907011,8254787,8822347,10322189,

%T 11329181,11354641,12307693,14528069,15801601,17757427,19023091,

%U 24995669,25871971

%N Primes p with f(p), f(f(p)), f(f(f(p))), f(f(f(f(p)))),  f(f(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="/A235984/b235984.txt">Table of n, a(n) for n = 1..19</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) = 501187 with 501187, f(501187) = 6886357, f(6886357) = 113948711, f(113948711) = 2224096873, f(2224096873) =  50351471977 and f(50351471977) = 1303792228393 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]]]]]&&PrimeQ[f[f[f[f[Prime[k]]]]]]&&PrimeQ[f[f[f[f[f[Prime[k]]]]]]]

%t n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10^7}]

%Y Cf. A000040, A234694, A234695, A235924, A235925, A235934, A235935.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 17 2014