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%I #24 Mar 29 2020 09:31:12
%S 7,13,37,97,103,223,307,457,853,877,1087,1297,1423,1483,1867,1993,
%T 2683,3457,4513,4783,5227,5647,6823,7873,8287,10453,13687,13873,15727,
%U 16057,16063,16183,17383,19417,19423,20743,21013,21313,22273,23053,23557
%N Primes followed by a [4,2,4] prime difference pattern of A001223.
%C The sequence includes A052166, A052168, A022008 and also other primes like 13, 103, 16063 etc.
%C 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)].
%C Analogous prime sequences are A047948, A052376, A052377 and A052188-A052198 with various [d, A052380(d/2), d] difference patterns following a(n).
%C All terms == 1 (mod 6) - _Zak Seidov_, Aug 27 2012
%C Subsequence of A022005. - _R. J. Mathar_, May 06 2017
%H Zak Seidov, <a href="/A052378/b052378.txt">Table of n, a(n) for n = 1..2000</a>
%F 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].
%e 103 initiates [103,107,109,113] prime quadruple followed by [4,2,4] difference pattern.
%t a = {}; Do[If[Prime[x + 3] - Prime[x] == 10, AppendTo[a, Prime[x]]], {x, 1, 10000}]; a - _Zerinvary Lajos_, Apr 03 2007
%t Select[Partition[Prime[Range[3000]],4,1],Differences[#]=={4,2,4}&][[All,1]] (* _Harvey P. Dale_, Jun 16 2017 *)
%o (PARI) is(n)=n%6==1 && isprime(n+4) && isprime(n+6) && isprime(n+10) && isprime(n) \\ _Charles R Greathouse IV_, Apr 29 2015
%Y Cf. A023200, A053320, A022008, A052166, A052168, A001223, A052380.
%K nonn
%O 1,1
%A _Labos Elemer_, Mar 22 2000
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