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%I #14 Nov 20 2022 04:57:07
%S 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,
%T 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,
%U 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
%N Number of 0's following directly the first 1 in the binary representation of n.
%H Robert Israel, <a href="/A290255/b290255.txt">Table of n, a(n) for n = 1..10000</a>
%F a(2^k)= k (k>=0); otherwise, a(n) = a(floor(n/2)).
%F 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
%e a(19) = 2 because 19_2 = 10'0'11; a(21) = 1 because 21_2 = 10'101_2 (the counted 0's are marked).
%p 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);
%p # Alternate:
%p f := proc(n) option remember; local v;
%p v:= padic:-ordp(n,2);
%p if n = 2^v then v else procname((n-2^v)/2^(v+1)) fi
%p end proc:
%p map(f, [$1..1000]); # _Robert Israel_, Sep 03 2017
%t 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 *)
%K nonn,base
%O 1,4
%A _Emeric Deutsch_, Sep 03 2017
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