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A236464 Primes p with prime(p) + 2 and prime(p) + 6 both prime. 8
3, 5, 7, 13, 43, 89, 313, 613, 643, 743, 1171, 1279, 1627, 1823, 1867, 1999, 2311, 2393, 2683, 2753, 2789, 3571, 4441, 4561, 5039, 5231, 5647, 5953, 6067, 6317, 6899, 8039, 8087, 8753, 8923, 9337, 9787, 9931, 10259, 10667 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to the conjecture in A236472, this sequence contains infinitely many terms, i.e., there are infinitely many prime triples of the form {prime(p), prime(p) + 2, prime(p) + 6} with p prime.

See A236462 for a similar sequence.

LINKS

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

EXAMPLE

a(1) = 3 since 3, prime(3) + 2 = 7 and prime(3) + 6 = 11 are all prime, but prime(2) + 6 = 9 is composite.

MATHEMATICA

p[n_]:=p[n]=PrimeQ[Prime[n]+2]&&PrimeQ[Prime[n]+6]

n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}]

CROSSREFS

Cf. A000040, A022004, A236457, A236458, A236462, A236472.

Sequence in context: A057187 A163080 A141414 * A064268 A235873 A118743

Adjacent sequences:  A236461 A236462 A236463 * A236465 A236466 A236467

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 26 2014

STATUS

approved

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Last modified October 14 09:57 EDT 2019. Contains 327995 sequences. (Running on oeis4.)