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A186634 Irregular triangle, read by rows, giving dense patterns of n primes. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

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.

LINKS

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

EXAMPLE

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

CROSSREFS

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

KEYWORD

nonn,tabf

AUTHOR

T. D. Noe, Feb 24 2011

STATUS

approved

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)