A235935 Primes p with f(p), f(f(p)), f(f(f(p))), f(f(f(f(p)))) all prime, where f(n) = prime(n) - n + 1.

2, 3, 2861, 8753, 56821, 83449, 162787, 165883, 167197, 186397, 217309, 261721, 275939, 309493, 355571, 382351, 467293, 501187, 539303, 560029, 602839, 640307, 657299, 708959, 879859, 919129, 973813, 1057741, 1085779, 1115899, 1156031, 1302667, 1366297, 1396427, 1516279, 1580461, 1760419, 1829797, 1867249, 1870021

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) = 2861 with 2861, f(2861) = 23143, f(23143) = 240769 and f(240769) = 3117791 and f(3117791) =  48951967 all prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..100
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

Cf. A000040, A234695, A235925, A235934.

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]]]]]]
n=0;Do[If[p[k],n=n+1;Print[n," ",Prime[k]]],{k,1,100000}]