%I #33 Feb 28 2023 09:45:50
%S 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,
%T 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,
%U 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
%N Irregular triangle, read by rows, giving dense patterns of n primes.
%C 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.
%C 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.
%H T. D. Noe, <a href="/A186634/b186634.txt">Rows n = 2..20, flattened</a> (from Forbes)
%H Thomas J. Engelsma, <a href="http://www.opertech.com/primes/k-tuples.html">Permissible Patterns</a>
%H Tony Forbes, <a href="http://www.ams.org/journals/mcom/1999-68-228/S0025-5718-99-01117-5/S0025-5718-99-01117-5.pdf">Prime clusters and Cunningham chains,</a> Math. Comp. 68 (1999), 1739-1747.
%H Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktmin.txt">Smallest Prime k-tuples</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>
%e The irregular triangle begins:
%e 0, 2
%e 0, 2, 6, 0, 4, 6
%e 0, 2, 6, 8
%e 0, 2, 6, 8, 12, 0, 4, 6, 10, 12
%e 0, 4, 6, 10, 12, 16
%e 0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20
%Y 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.
%K nonn,tabf
%O 2,2
%A _T. D. Noe_, Feb 24 2011