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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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%I #21 Oct 08 2019 20:05:00

%S 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,

%T 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,

%U 0,0,0,0,16,0,1,1,1,1,17,0,0,2,2,2,18,0,1

%N 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).

%H Peter Kagey, <a href="/A309576/b309576.txt">Table of n, a(n) for n = 1..9987</a> (first 1000 rows)

%F T(n,0) = 0 and T(n, A070939(n)) = n.

%e 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.

%e Table begins:

%e n\k| 0 1 2 3 4

%e ---+-----------

%e 1 | 0 1

%e 2 | 0 0 2

%e 3 | 0 1 3

%e 4 | 0 0 0 4

%e 5 | 0 1 1 5

%e 6 | 0 0 2 6

%e 7 | 0 1 3 7

%e 8 | 0 0 0 0 8

%e 9 | 0 1 1 1 9

%t 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 *)

%o (Ruby)

%o def t(n,k); n & (1 << k) - 1 end

%Y Cf. A070939, A309577.

%K nonn,tabf,base,look

%O 1,5

%A _Peter Kagey_, Aug 08 2019