A235984 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.

2, 3, 501187, 560029, 2076881, 2836003, 2907011, 8254787, 8822347, 10322189, 11329181, 11354641, 12307693, 14528069, 15801601, 17757427, 19023091, 24995669, 25871971

Offset: 1

Author

Zhi-Wei Sun, Jan 17 2014

Keywords

• nonn

Comments

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

Examples

			a(3) = 501187 with 501187, f(501187) = 6886357, f(6886357) = 113948711, f(113948711) = 2224096873, f(2224096873) =  50351471977 and f(50351471977) = 1303792228393 all prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..19
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

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

Programs

Mathematica

f[n_]:=Prime[n]-n+1
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]]]]]]]
n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,10^7}]