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%I #22 Aug 20 2017 23:31:19
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,28,
%T 29,30,31,32,33,35,36,39,42,43,45,46,47,48,49,51,53,54,55,56,57,58,59,
%U 60,61,62,63,64,65,67,71,73,76,79,85,86,87,90,91,93,94,95,96,97,99,100
%N A positive integer n is included if all runs of 0's in binary n are of the same length.
%C Clarification: A binary number consists of "runs" completely of 1's alternating with runs completely of 0's. No two or more runs all of the same digit are adjacent.
%C This sequence contains in part positive integers that each contain one run of 0's. For those members of this sequence each with at least two runs of 0's, see A164712.
%C Number of terms with n binary digits is A243815(n-1). - _Robert Israel_, Nov 09 2015
%H Ivan Neretin, <a href="/A164710/b164710.txt">Table of n, a(n) for n = 1..10000</a>
%p isA164710 := proc(n) local bdg,arl,lset ; bdg := convert(n,base,2) ; lset := {} ; arl := -1 ; for p from 1 to nops(bdg) do if op(p,bdg) = 0 then if p = 1 then arl := 1 ; else arl := arl+1 ; end if; else if arl > 0 then lset := lset union {arl} ; end if; arl := 0 ; end if; end do ; if arl > 0 then lset := lset union {arl} ; end if; return (nops(lset) <= 1 ); end proc: for n from 1 to 300 do if isA164710(n) then printf("%d,",n) ; end if; end do; # _R. J. Mathar_, Feb 27 2010
%p F:= proc(d)
%p local res,r,m,e,C,M;
%p res:= [1$d];
%p for r from 1 to floor(d/2) do
%p for m from 1 to floor(d/r)-1 do
%p e:= d - r*(m+1);
%p for C in combinat:-choose(e+r,e) do
%p M:= subsop(op(map(`=`,C,1)),[0$(e+r)]);
%p res:= res, subs(0 = (1,0$m), M);
%p od
%p od
%p od;
%p sort(map(t -> add(t[-i]*2^(i-1),i=1..d), [res]));
%p end proc:
%p N:= 10: # to get all terms < 2^N
%p map(op,[seq(F(d),d=1..N)]); # _Robert Israel_, Nov 09 2015
%t Select[Range@ 100, SameQ @@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 0 &]] &] (* _Michael De Vlieger_, Aug 20 2017 *)
%o (Perl)
%o foreach(1..100){
%o %runs=();
%o $runs{$_}++ foreach split /1+/, sprintf("%b",$_);
%o delete $runs{''};
%o print "$_, " if 1>=keys(%runs);
%o }
%o # _Ivan Neretin_, Nov 09 2015
%Y Cf. A164707, A164711, A164712, A243815.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Aug 23 2009
%E Terms beyond 39 by _R. J. Mathar_, Feb 27 2010
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