A144789 - OEIS

%I #16 Apr 06 2020 19:35:23

%S 0,1,0,2,1,1,0,3,2,1,1,2,1,1,0,4,3,1,2,1,1,1,1,3,2,1,1,2,1,1,0,5,4,1,

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

%U 1,1,3,2,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,4,1,3,2,1,1,2,1,1

%N Consider the runs of 0's in the binary representation of n, each of these runs being on the edge of the binary representation n and/or being bounded by 1's. a(n) = the length of the shortest such run (with positive length) of 0's in binary n. a(n) = 0 if there are no runs of 0's in binary n.

%e 20 in binary is 10100. The runs of 0's are as follows: 1(0)1(00). The shortest of these runs contains exactly one 0's So a(20) = 1.

%p A007814 := proc(n) local nshf,a ; a := 0 ; nshf := n ; while nshf mod 2 = 0 do nshf := nshf/2 ; a := a+1 ; od: a ; end: A144789 := proc(n) option remember ; local lp2,lp2sh,bind ; bind := convert(n,base,2) ; if add(i,i=bind) = nops(bind) then RETURN(0) ; fi; lp2 := A007814(n) ; if lp2 = 0 then A144789(floor(n/2)) ; else lp2sh := A144789(n/2^lp2) ; if lp2sh = 0 then lp2 ; else min(lp2,lp2sh) ; fi; fi; end: for n from 1 to 140 do printf("%d,",A144789(n)) ; od: # _R. J. Mathar_, Sep 29 2008

%t Table[Min[Length/@Select[Split[IntegerDigits[n,2]],MemberQ[#,0]&]],{n,120}]/.\[Infinity]->0 (* _Harvey P. Dale_, Jul 24 2016 *)

%Y Cf. A087117, A144790.

%K base,nonn

%O 1,4

%A _Leroy Quet_, Sep 21 2008

%E Extended by _R. J. Mathar_, Sep 29 2008