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).

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

Offset: 1

Author

Peter Kagey, Aug 08 2019

Keywords

• nonn
• tabf
• base

Examples

			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
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..9987 (first 1000 rows)

Crossrefs

Cf. A070939, A309576.

Programs

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 *)

Ruby

def t(n,k); n & (1 << n.bit_length - k) - 1 end

Formula

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