A236482 Primes p with p + 2, prime(p) + 2, prime(prime(p)) + 2 and prime(prime(prime(p))) + 2 all prime.

41609, 1119047, 1928621, 2348579, 2371709, 3406727, 4098569, 4204817, 4438997, 5561819, 6161159, 6293297, 8236439, 8736701, 8890667, 8951387, 9231329, 9390077, 10492457, 10619897, 11255729, 11514719, 11769479, 11920661, 12316697

Offset

1,1

Comments

According to the general conjecture in A236481, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Example

a(1) = 41609 with 41609, 41609 + 2 = 41611, prime(41609) + 2 = 500909 + 2 = 500911, prime(500909) + 2 = 7382957 + 2 = 7382959 and prime(7382957) + 2 = 130090109 + 2 = 130090111 all prime.

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]&&PrimeQ[Prime[Prime[Prime[n]]]+2]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10^6}]

Crossrefs

Cf. A000040, A001359, A006512, A236457, A236458, A236467, A236480, A236481, A236484.

Sequence in context: A165114 A002879 A207049 * A163392 A262801 A253681

Adjacent sequences: A236479 A236480 A236481 * A236483 A236484 A236485

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved