|
|
A164710
|
|
A positive integer n is included if all runs of 0's in binary n are of the same length.
|
|
7
|
|
|
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, 29, 30, 31, 32, 33, 35, 36, 39, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 73, 76, 79, 85, 86, 87, 90, 91, 93, 94, 95, 96, 97, 99, 100
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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.
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.
|
|
LINKS
|
|
|
MAPLE
|
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
F:= proc(d)
local res, r, m, e, C, M;
res:= [1$d];
for r from 1 to floor(d/2) do
for m from 1 to floor(d/r)-1 do
e:= d - r*(m+1);
for C in combinat:-choose(e+r, e) do
M:= subsop(op(map(`=`, C, 1)), [0$(e+r)]);
res:= res, subs(0 = (1, 0$m), M);
od
od
od;
sort(map(t -> add(t[-i]*2^(i-1), i=1..d), [res]));
end proc:
N:= 10: # to get all terms < 2^N
|
|
MATHEMATICA
|
Select[Range@ 100, SameQ @@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 0 &]] &] (* Michael De Vlieger, Aug 20 2017 *)
|
|
PROG
|
(Perl)
foreach(1..100){
%runs=();
$runs{$_}++ foreach split /1+/, sprintf("%b", $_);
delete $runs{''};
print "$_, " if 1>=keys(%runs);
}
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|