A161225 a(n) = number of distinct integers that can be constructed by removing one or more 0's from the binary representation of n, and concatenating while leaving the remaining digits in their same order.

0, 1, 0, 2, 1, 1, 0, 3, 2, 3, 1, 2, 1, 1, 0, 4, 3, 5, 2, 5, 3, 3, 1, 3, 2, 3, 1, 2, 1, 1, 0, 5, 4, 7, 3, 8, 5, 5, 2, 7, 5, 7, 3, 5, 3, 3, 1, 4, 3, 5, 2, 5, 3, 3, 1, 3, 2, 3, 1, 2, 1, 1, 0, 6, 5, 9, 4, 11, 7, 7, 3, 11, 8, 11, 5, 8, 5, 5, 2, 9, 7, 11, 5, 11, 7, 7, 3, 7, 5, 7, 3, 5, 3, 3, 1, 5, 4, 7, 3, 8, 5, 5, 2

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

20 in binary is 10100. By removing one, two, or three 0's from this, we can come up with these distinct integers written in binary: 1100, 1010, 110, 101, 11. There are five of these, so a(20) = 5.

Maple

g:= proc(n) n + 2^(ilog2(n)) end proc:
h:= proc(n) n + 2^(1+ilog2(n)) end proc:
f:= proc(n) option remember; local S, k, r;
      k:= ilog2(n)-1; r:= floor(n/2^k);
      if r = 2 then S:= procname(n-2^k); {n-2^k} union S union map(g, S)
      else map(h, procname(n - 2^(k+1)))
      fi
end proc:
f(1):= {}: f(2):= {1}:
seq(nops(f(n)), n=1..200); # Robert Israel, Apr 12 2020

Prog

(Magma) ndi:=function(n) a:=Intseq(n, 2); p:=1; c:=1; for j:=1 to #a do if a[j] eq 0 then c+:=1; else p*:=c; c:=1; end if; end for; return p-1; end function; [ ndi(n): n in [1..103] ]; // Klaus Brockhaus, Jun 10 2009

Crossrefs

Cf. A007088 (numbers written in base 2). - Klaus Brockhaus, Jun 10 2009

Sequence in context: A308451 A308067 A124748 * A174980 A277488 A325794

Adjacent sequences: A161222 A161223 A161224 * A161226 A161227 A161228

Keyword

base,nonn,look,hear

Author

Leroy Quet, Jun 06 2009

Extensions

Extended by Ray Chandler, Jun 09 2009

More terms from Klaus Brockhaus, Jun 10 2009

Status

approved