|
%I #7 Apr 06 2020 22:12:52
%S 0,0,1,0,2,0,0,0,3,0,1,0,0,0,0,0,4,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,5,0,
%T 1,0,2,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,1,0,
%U 2,0,0,0,2,0,1,0,0,0,0,0,1,0,1,0,1,0,0
%N Length of shortest run of zeros after a one in the binary expansion of n. a(0) = 0.
%F For n > 0, a(n) = A333768(n) - 1.
%e The binary expansion of 148 is (1,0,0,1,0,1,0,0), so a(148) = 1.
%t stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t Table[If[n==0,0,Min@@stc[n]-1],{n,0,100}]
%Y Positions of first appearances (ignoring index 0) are A000079.
%Y Positions of terms > 0 are A022340.
%Y Minimum prime index is A055396.
%Y The maximum part minus 1 is given by A087117.
%Y All of the following pertain to compositions in standard order (A066099):
%Y - Length is A000120.
%Y - Compositions without 1's are A022340.
%Y - Sum is A070939.
%Y - Product is A124758.
%Y - Runs are counted by A124767.
%Y - Strict compositions are A233564.
%Y - Constant compositions are A272919.
%Y - Runs-resistance is A333628.
%Y - Maximum is A333766.
%Y - Minimum is A333768.
%Y - Weakly decreasing compositions are A114994.
%Y - Weakly increasing compositions are A225620.
%Y - Strictly decreasing compositions are A333255.
%Y - Strictly increasing compositions are A333256.
%Y Cf. A029931, A048793, A228351, A328594, A333217, A333218, A333219, A333632.
%K nonn
%O 0,5
%A _Gus Wiseman_, Apr 06 2020
|
