A236119 Primes p with prime(p) - p - 1 and prime(p) - p + 1 both prime.

5, 17, 23, 41, 71, 83, 173, 293, 337, 353, 563, 571, 719, 811, 911, 953, 1201, 1483, 1579, 1877, 2081, 2089, 2309, 2579, 2749, 2803, 3329, 3343, 3511, 3691, 3779, 3851, 3881, 3907, 4021, 4049, 4093, 4657, 4813, 5051, 5179, 5333, 5519, 5591, 6053, 6547, 6841, 7151, 7723, 8209

Offset

1,1

Comments

By the conjecture in A236097, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Example

a(1) = 5 since neither prime(2) - 2 - 1 = 0 nor prime(3) - 3 - 1 = 1 is prime, but prime(5) - 5 - 1 = 5 and prime(5) - 5 + 1 = 7 are both prime.

Mathematica

p[n_]:=PrimeQ[Prime[n]-n-1]&&PrimeQ[Prime[n]-n+1]
n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1100}]

Prog

(PARI) s=[]; forprime(p=2, 10000, if(isprime(prime(p)-p-1) && isprime(prime(p)-p+1), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014

Crossrefs

Cf. A000040, A001359, A006512, A014574, A234695, A235925, A236097.

Sequence in context: A019410 A133423 A154632 * A141275 A303193 A145043

Adjacent sequences: A236116 A236117 A236118 * A236120 A236121 A236122

Keyword

nonn

Author

Zhi-Wei Sun, Jan 19 2014

Status

approved