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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Subsequence of A031924.

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

Cf. A078853, A046789.

Cf. A001223, A033451, A052197, A052198.

Sequence in context: A044379 A044760 A142505 * A142529 A288022 A142634

Adjacent sequences: A047945 A047946 A047947 * A047949 A047950 A047951

Keyword

easy,nonn

Author

Enoch Haga

Extensions

Corrected by T. D. Noe, Mar 07 2008

Status

approved