A290255 Number of 0's following directly the first 1 in the binary representation of n.

0, 1, 0, 2, 1, 0, 0, 3, 2, 1, 1, 0, 0, 0, 0, 4, 3, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,4

Links

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

Formula

a(2^k)= k (k>=0); otherwise, a(n) = a(floor(n/2)).

G.f. q(x) + Sum_{j>=1} q(x^(2^j))*(x^(2^j)-x^(2^(j-1)))/(x-1) where q(z) = Sum_{j>=1} j*x^(2^j). - Robert Israel, Sep 03 2017

Example

a(19) = 2 because 19_2 = 10'0'11; a(21) = 1 because 21_2 = 10'101_2 (the counted 0's are marked).

Maple

a := proc (n) if type(log[2](n), integer) = true then log[2](n) else a(floor((1/2)*n)) end if end proc: seq(a(n), n = 1 .. 200);
# Alternate:
f := proc(n) option remember; local v;
v:= padic:-ordp(n, 2);
  if n = 2^v then v else procname((n-2^v)/2^(v+1)) fi
end proc:
map(f, [$1..1000]); # Robert Israel, Sep 03 2017

Mathematica

sfo[n_]:=Module[{sidn2=Split[IntegerDigits[n, 2]]}, If[Length[ sidn2[[1]]]> 1, 0, Length[ sidn2[[2]]]]]; Join[{0}, Array[sfo, 110, 2]] (* Harvey P. Dale, Mar 04 2018 *)

Crossrefs

Sequence in context: A037854 A362633 A091229 * A283982 A370883 A173402

Adjacent sequences: A290252 A290253 A290254 * A290256 A290257 A290258

Keyword

nonn,base

Author

Emeric Deutsch, Sep 03 2017

Status

approved