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A309576
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Table read by rows: T(n, k) is the last k bits of n interpreted as a base-2 representation of a number and converted to decimal, 0 <= k <= A070939(n).
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2
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0, 1, 0, 0, 2, 0, 1, 3, 0, 0, 0, 4, 0, 1, 1, 5, 0, 0, 2, 6, 0, 1, 3, 7, 0, 0, 0, 0, 8, 0, 1, 1, 1, 9, 0, 0, 2, 2, 10, 0, 1, 3, 3, 11, 0, 0, 0, 4, 12, 0, 1, 1, 5, 13, 0, 0, 2, 6, 14, 0, 1, 3, 7, 15, 0, 0, 0, 0, 0, 16, 0, 1, 1, 1, 1, 17, 0, 0, 2, 2, 2, 18, 0, 1
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OFFSET
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1,5
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LINKS
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FORMULA
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T(n,0) = 0 and T(n, A070939(n)) = n.
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EXAMPLE
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For n = 26 and k = 3, T(26, 3) = 2 because 26 = 11010_2, and looking at only the last three bits gives 010_2 = 2.
Table begins:
n\k| 0 1 2 3 4
---+-----------
1 | 0 1
2 | 0 0 2
3 | 0 1 3
4 | 0 0 0 4
5 | 0 1 1 5
6 | 0 0 2 6
7 | 0 1 3 7
8 | 0 0 0 0 8
9 | 0 1 1 1 9
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MATHEMATICA
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T[n_, k_] := BitAnd[n, 2^k-1]; Table[T[n, k], {n, 1, 20}, {k, 0, BitLength[n]}] // Flatten (* Amiram Eldar, Aug 09 2019 *)
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PROG
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(Ruby)
def t(n, k); n & (1 << k) - 1 end
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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