A309576 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).
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
Offset: 1
Examples
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
Links
- Peter Kagey, Table of n, a(n) for n = 1..9987 (first 1000 rows)
Programs
-
Mathematica
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 *) -
Ruby
def t(n,k); n & (1 << k) - 1 end
Formula
T(n,0) = 0 and T(n, A070939(n)) = n.