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Search: id:A052378
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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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+0
18
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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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 (zerinvarylajos(AT)yahoo.com), Apr 03 2007
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CROSSREFS
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Cf. A023200, A053320, A022008, A052166, A052168, A053320, A001223, A052380.
Sequence in context: A118819 A118525 A094069 this_sequence A090607 A123250 A062591
Adjacent sequences: A052375 A052376 A052377 this_sequence A052379 A052380 A052381
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 22 2000
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