A186634 Irregular triangle, read by rows, giving dense patterns of n primes.

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

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 Weisstein's World of Mathematics, 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 * A363910 A139213 A344873

Adjacent sequences: A186631 A186632 A186633 * A186635 A186636 A186637

Keyword

nonn,tabf

Author

T. D. Noe, Feb 24 2011

Status

approved