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A236481 Primes p with p + 2, prime(p) + 2 and prime(prime(p)) + 2 all prime. 5
3, 1949, 4217, 8219, 9929, 22091, 23537, 28097, 38711, 41609, 50051, 60899, 68111, 72227, 74159, 79631, 115151, 122399, 127679, 150959, 155537, 266687, 267611, 270551, 271499, 284741, 306347, 428297, 433661, 444287 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: For any positive integer m, there are infinitely many chains p(1) < p(2) < ... < p(m) of m primes with p(k) + 2 prime for all k = 1,...,m such that p(k + 1) = prime(p(k)) for every 0 < k < m.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..5000

Zhi-Wei Sun, A new kind of prime chains, a message to Number Theory List, Jan. 20, 2014.

EXAMPLE

a(1) = 3 since 3, 3 + 2 = 5, prime(3) + 2 = 7 and prime(prime(3)) + 2 = prime(5) + 2 = 13 are all prime, but 2 + 2 = 4 is composite.

MATHEMATICA

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]

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

CROSSREFS

Cf. A000010, A000040, A001359, A006512, A235925, A236066, A236457, A236458, A236468, A236470, A236480, A236482, A236484.

Sequence in context: A172940 A096730 A255862 * A307928 A193149 A024047

Adjacent sequences:  A236478 A236479 A236480 * A236482 A236483 A236484

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 26 2014

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)