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Search: id:A122872
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| A122872 |
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Table by antidiagonals, T(n,k) is k-th number that starts with n in binary representation. |
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+0
1
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| 1, 2, 2, 3, 4, 3, 4, 5, 6, 4, 5, 8, 7, 8, 5, 6, 9, 12, 9, 10, 6, 7, 10, 13, 16, 11, 12, 7, 8, 11, 14, 17, 20, 13, 14, 8, 9, 16, 15, 18, 21, 24, 15, 16, 9, 10, 17, 24, 19, 22, 25, 28, 17, 18, 10, 11, 18, 25, 32, 23, 26, 29, 32, 19, 20, 11, 12, 19, 26, 33, 40, 27, 30, 33, 36, 21, 22, 12
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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In rows n through 2n-1, every integer >= n occurs exactly once.
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FORMULA
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T(n,1) = n; T(n,2k) = 2T(n,k); T(n,2k+1) = 2T(n,k) + 1. T(n,k) = k + (n-1) * 2^floor(log_2(k)) = k + (n-1)*A053644(k).
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EXAMPLE
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Top left corner is:
1 2 3 4 5
2 4 5 8 9
3 6 7 12 13
4 8 9 16 17
5 10 11 20 21
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CROSSREFS
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Rows: A000027, A004754, A004755, A004756, A004757, A004758, A004759. Algebraically, A053645 would be row zero, minus A080079 would be row minus one. See also A053644.
Adjacent sequences: A122869 A122870 A122871 this_sequence A122873 A122874 A122875
Sequence in context: A106251 A134478 A051162 this_sequence A132919 A032355 A091257
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 23 2006
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