|
|
A309577
|
|
Table read by rows: T(n, k) is n with the first k bits removed from its binary expansion and then converted back to decimal, for 0 <= k <= A070939(n).
|
|
2
|
|
|
1, 0, 2, 0, 0, 3, 1, 0, 4, 0, 0, 0, 5, 1, 1, 0, 6, 2, 0, 0, 7, 3, 1, 0, 8, 0, 0, 0, 0, 9, 1, 1, 1, 0, 10, 2, 2, 0, 0, 11, 3, 3, 1, 0, 12, 4, 0, 0, 0, 13, 5, 1, 1, 0, 14, 6, 2, 0, 0, 15, 7, 3, 1, 0, 16, 0, 0, 0, 0, 0, 17, 1, 1, 1, 1, 0, 18, 2, 2, 2, 0, 0, 19
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
T(n,0) = n and T(n, A070939(n)) = 0.
|
|
EXAMPLE
|
For n = 26 and k = 2, T(26, 2) = 2 because 26 = 11010_2, and removing the first two bits leaves 010_2 = 2.
Table begins:
n\k| 0 1 2 3 4
---+-----------
1 | 1 0
2 | 2 0 0
3 | 3 1 0
4 | 4 0 0 0
5 | 5 1 1 0
6 | 6 2 0 0
7 | 7 3 1 0
8 | 8 0 0 0 0
9 | 9 1 1 1 0
|
|
MATHEMATICA
|
T[n_, k_] := BitAnd[n, 2^k-1]; Table[T[n, k], {n, 1, 20}, {k, BitLength[n], 0, -1}] // Flatten (* Amiram Eldar, Aug 09 2019 *)
|
|
PROG
|
(Ruby)
def t(n, k); n & (1 << n.bit_length - k) - 1 end
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|