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A052378
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Primes followed by a [4,2,4] prime difference pattern of A001223.
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22
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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
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OFFSET
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1,1
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COMMENTS
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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)].
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LINKS
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FORMULA
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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].
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EXAMPLE
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103 initiates [103,107,109,113] prime quadruple followed by [4,2,4] difference pattern.
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(n)=n%6==1 && isprime(n+4) && isprime(n+6) && isprime(n+10) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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