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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

1. The sequence includes A052166, A052168, A022008 and also other primes like 13, 103, 16063 etc. 2. 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)]. 3. Analogous prime sequences are A047948, A052376, A052377 and A052188-A052199 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

Cf. A023200, A053320, A022008, A052166, A052168, A001223, A052380.

Sequence in context: A118525 A213537 A094069 * A090607 A201597 A158375

Adjacent sequences:  A052375 A052376 A052377 * A052379 A052380 A052381

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 22 2000

STATUS

approved

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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.