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

2, 3, 23, 311, 1777, 2341, 2861, 3329, 3833, 4051, 8753, 9007, 11587, 13093, 13309, 14551, 16001, 19687, 23143, 26993, 37309, 41981, 44131, 45491, 54623, 56431, 56821, 57991, 60223, 61643, 66413, 66883, 67511, 68767, 69029, 70003, 75743, 76261, 76819, 80021

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) = 23 with 23, f(23) = 61, f(61) = 223 and f(223) = 1187 all prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..2000
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

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

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