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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.
27
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.
Sequence in context: A044379 A044760 A142505 * A142529 A288022 A142634
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Corrected by T. D. Noe, Mar 07 2008
STATUS
approved