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A052378 Primes followed by a [4,2,4] prime difference pattern of A001223. 22
7, 13, 37, 97, 103, 223, 307, 457, 853, 877, 1087, 1297, 1423, 1483, 1867, 1993, 2683, 3457, 4513, 4783, 5227, 5647, 6823, 7873, 8287, 10453, 13687, 13873, 15727, 16057, 16063, 16183, 17383, 19417, 19423, 20743, 21013, 21313, 22273, 23053, 23557 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The sequence includes A052166, A052168, A022008 and also other primes like 13, 103, 16063 etc.
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
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
Sequence in context: A213537 A094069 A338812 * A090607 A201597 A158375
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 22 2000
STATUS
approved

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)