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

1,1

Comments

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

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

Example

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

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}]

Crossrefs

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

Sequence in context: A139067 A099656 A157733 * A064888 A104458 A191859

Adjacent sequences: A235931 A235932 A235933 * A235935 A235936 A235937

Keyword

nonn

Author

Zhi-Wei Sun, Jan 17 2014

Status

approved