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A113821
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Triangle where a(1,1)=1; and the n terms of row n are the smallest positive integers not occurring earlier in the sequence such that, for any given m (1 <= m <= n), a(n,m) and n have at least one 1-bit in the same position when they are written in binary.
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7
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1, 2, 3, 5, 6, 7, 4, 12, 13, 14, 9, 11, 15, 17, 19, 10, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 8, 24, 40, 41, 42, 43, 44, 45, 33, 35, 37, 39, 46, 47, 49, 51, 53, 34, 38, 50, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 36, 52, 68, 74, 75, 76, 77
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OFFSET
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1,2
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COMMENTS
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Sequence is a permutation of the positive integers.
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LINKS
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EXAMPLE
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4 = 100 in binary. Among the positive integers not occurring among the first 3 rows of the sequence (4 = 100 in binary, 8 = 1000 in binary, 9 = 1001 in binary, etc...), [4,12,13,14] (which is [100,1100,1101,1110] in binary) are the lowest 4 positive integers that share at least one 1-bit with 4 when written in binary. So row 4 is [4,12,13,14].
Triangle begins:
1
2 3
5 6 7
4 12 13 14
9 11 15 17 19
10 18 20 21 22 23
25 26 27 28 29 30 31
8 24 40 41 42 43 44 45
33 35 37 39 46 47 49 51 53
34 38 50 54 55 56 57 58 59 60
61 62 63 65 66 67 69 70 71 72 73
36 52 68 74 75 76 77 78 79 84 85 86
...
(End)
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MATHEMATICA
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Block[{a = {{1}}}, Do[a = Join[a, {Take[#, n]}] &@ Select[Flatten@ Position[Array[BitAnd[n, #] &, 120], k_ /; k > 0], FreeQ[a, #] &], {n, 2, 12}]; Flatten@ a] (* Michael De Vlieger, Aug 16 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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