OFFSET
1,1
COMMENTS
a(n) is the lesser term of a 4-twin (A023200) after which the next 4-twin comes in minimal distance [here it is 2; see A052380(4/2)].
Analogous prime sequences are A047948, A052376, A052377 and A052188-A052198 with various [d, A052380(d/2), d] difference patterns following a(n).
All terms == 1 (mod 6) - Zak Seidov, Aug 27 2012
Subsequence of A022005. - R. J. Mathar, May 06 2017
LINKS
Zak Seidov, Table of n, a(n) for n = 1..2000
FORMULA
a(n) is the initial prime of a [p, p+4, p+6, p+6+4] prime-quadruple consisting of two 4-twins: [p, p+4] and [p+6, p+10].
EXAMPLE
103 initiates [103,107,109,113] prime quadruple followed by [4,2,4] difference pattern.
MATHEMATICA
a = {}; Do[If[Prime[x + 3] - Prime[x] == 10, AppendTo[a, Prime[x]]], {x, 1, 10000}]; a (* Zerinvary Lajos, Apr 03 2007 *)
Select[Partition[Prime[Range[3000]], 4, 1], Differences[#]=={4, 2, 4}&][[All, 1]] (* Harvey P. Dale, Jun 16 2017 *)
PROG
(PARI) is(n)=n%6==1 && isprime(n+4) && isprime(n+6) && isprime(n+10) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 22 2000
STATUS
approved