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A186634
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Irregular triangle, read by rows, giving dense patterns of n primes.
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3
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0, 2, 0, 2, 6, 0, 4, 6, 0, 2, 6, 8, 0, 2, 6, 8, 12, 0, 4, 6, 10, 12, 0, 4, 6, 10, 12, 16, 0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20, 0, 2, 6, 8, 12, 18, 20, 26, 0, 2, 6, 12, 14, 20, 24, 26, 0, 6, 8, 14, 18, 20, 24, 26, 0, 2, 6, 8, 12, 18, 20, 26, 30, 0, 2, 6, 12, 14, 20, 24, 26, 30, 0, 4, 6, 10, 16, 18, 24, 28, 30, 0, 4, 10, 12, 18, 22, 24, 28, 30, 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 0, 2, 6, 12, 14, 20, 24, 26, 30, 32
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OFFSET
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2,2
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COMMENTS
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The first pattern (0,2) is for twin primes (p,p+2). Row n contains A083409(n) patterns, each one consisting of 0 followed by n-1 terms. In each row the patterns are in lexicographic order.
These numbers (in a slightly different order) appear in Table 1 of the paper by Tony Forbes. Sequence A186702 gives the least prime starting a given pattern.
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LINKS
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T. D. Noe, Rows n = 2..20, flattened (from Forbes)
Thomas J. Engelsma, Permissible Patterns
Tony Forbes, Prime clusters and Cunningham chains, Math. Comp. 68 (1999), 1739-1747.
Tony Forbes, Smallest Prime k-tuples
Eric W. Weisstein, MathWorld: Prime Constellation
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EXAMPLE
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The irregular triangle begins:
0, 2
0, 2, 6, 0, 4, 6
0, 2, 6, 8
0, 2, 6, 8, 12, 0, 4, 6, 10, 12
0, 4, 6, 10, 12, 16
0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20
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CROSSREFS
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Cf. A020497, A008407, A186702, and sequences created by these patterns: A001359, A022004, A022005, A007530, A022006, A022007, A022008, A022009, A022010, A022011, A022012, A022013, A022545, A022546, A022547, A022548, A027569, A027570.
Sequence in context: A265882 A324253 A208385 * A139213 A344873 A306079
Adjacent sequences: A186631 A186632 A186633 * A186635 A186636 A186637
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KEYWORD
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nonn,tabf
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AUTHOR
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T. D. Noe, Feb 24 2011
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STATUS
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approved
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