A047948 Smallest of three consecutive primes with a difference of 6: primes p such that p+6 and p+12 are the next two primes.

47, 151, 167, 251, 257, 367, 557, 587, 601, 647, 727, 941, 971, 1097, 1117, 1181, 1217, 1361, 1741, 1747, 1901, 2281, 2411, 2671, 2897, 2957, 3301, 3307, 3631, 3727, 4007, 4451, 4591, 4651, 4987, 5101, 5107, 5297, 5381, 5387, 5557, 5801, 6067, 6257, 6311, 6317

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn

Comments

Let p(k) be the k-th prime; sequence gives p(k) such that p(k+2) - p(k+1) = p(k+1) - p(k) = 6.

Examples

			47 is a term as the next two primes are 53 and 59.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Subsequence of A031924.

A033451 (four consecutive primes with difference 6) is a subsequence.

Cf. A078853, A046789.

Cf. A001223, A033451, A052197, A052198.

Programs

Mathematica

ok[p_] := (q = NextPrime[p]) == p+6 && NextPrime[q] == q+6; Select[Prime /@ Range[1000], ok][[;; 45]] (* Jean-François Alcover, Jul 11 2011 *)
Transpose[Select[Partition[Prime[Range[1000]],3,1],Differences[#]=={6,6}&]] [[1]] (* Harvey P. Dale, Apr 25 2014 *)

PARI

is_A047948(n)={nextprime(n+1)==n+6 && nextprime(n+7)==n+12 && isprime(n)} \\ Charles R Greathouse IV, Aug 17 2011, simplified by M. F. Hasler, Jan 13 2013

PARI

p=2;q=3;forprime(r=5,1e4,if(r-p==12&&q-p==6,print1(p", "));p=q;q=r) \\ Charles R Greathouse IV, Aug 17 2011

Extensions

Corrected by T. D. Noe, Mar 07 2008