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A052380
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a(n)=D is the smallest distance (D) between 2 non-overlapping prime-twins differing by d=2n; these twins are [p,p+d] or [p+D,p+D+d] and p>3.
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14
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6, 6, 6, 12, 12, 12, 18, 18, 18, 24, 24, 24, 30, 30, 30, 36, 36, 36, 42, 42, 42, 48, 48, 48, 54, 54, 54, 60, 60, 60, 66, 66, 66, 72, 72, 72, 78, 78, 78, 84, 84, 84, 90, 90, 90, 96, 96, 96, 102, 102, 102, 108, 108, 108, 114, 114, 114, 120, 120, 120, 126, 126, 126, 132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For d=D the quadruple of primes becomes a triple: [p,p+d],[p+d,p+2d].
Without the p>3 condition, a(1)=2
The starter prime p, is followed by a prime d-pattern of [d,D-d,d], where D-d=a(n)-2n is 4,2 or 0; these d-patterns are as follows: [2,4,2],[4,2,4],[6,6],[8,4,8],[10,2,10],[12,12], etc.
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FORMULA
| a(n)=6*Ceiling[n/3]=6*Ceiling[d/6]=D=D(n).
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EXAMPLE
| n=5,d=2n=10, the minimal distance for 10-twins is 12 (see A031928, d=10) the smallest term in A053323. It is occurs first between twins of [409,419] and [421,431]; see 409=A052354(1)=A052376(1)=A052381(5).
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CROSSREFS
| See also A001223, A031924-A031938, A053319-A053331, A052350-A052358.
Sequence in context: A186983 A046264 A035019 * A180604 A109047 A153171
Adjacent sequences: A052377 A052378 A052379 * A052381 A052382 A052383
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Mar 13 2000
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