This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186634 #34 Feb 16 2025 08:33:14 %S A186634 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 A186634 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 A186634 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 A186634 Irregular triangle, read by rows, giving dense patterns of n primes. %C A186634 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 A186634 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 A186634 T. D. Noe, <a href="/A186634/b186634.txt">Rows n = 2..20, flattened</a> (from Forbes) %H A186634 Thomas J. Engelsma, <a href="http://www.opertech.com/primes/k-tuples.html">Permissible Patterns</a> %H A186634 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 A186634 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktmin.txt">Smallest Prime k-tuples</a> %H A186634 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a> %e A186634 The irregular triangle begins: %e A186634 0, 2 %e A186634 0, 2, 6, 0, 4, 6 %e A186634 0, 2, 6, 8 %e A186634 0, 2, 6, 8, 12, 0, 4, 6, 10, 12 %e A186634 0, 4, 6, 10, 12, 16 %e A186634 0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20 %Y A186634 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 A186634 nonn,tabf %O A186634 2,2 %A A186634 _T. D. Noe_, Feb 24 2011