

A121539


Numbers whose binary expansion ends in an even number of 1's.


24



0, 2, 3, 4, 6, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 32, 34, 35, 36, 38, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 88, 90, 91, 92, 94, 96, 98, 99, 100
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Equivalently, increasing sequence defined by: "if k appears a*k+b does not", case a(1)=0, a=2, b=1.
Every even number ends with zero 1's and zero is even, so every even number is a term.
Consists of all even numbers together with A131323.


LINKS



FORMULA



EXAMPLE

11 in binary is 1011, which ends with two 1's.


MATHEMATICA

s={2}; With[{a=2, b=1}, Do[If[FreeQ[s, (nb)/a], AppendTo[s, n]], {n, 3, 100}]]; s


PROG

(Haskell)
import Data.List (elemIndices)
a121539 n = a121539_list !! (n1)
a121539_list = elemIndices 1 a035263_list
(Magma) [n: n in [0..200]  Valuation(n+1, 2) mod 2 eq 0 ]; // Vincenzo Librandi, Apr 16 2015
(Python)
def ok(n): b = bin(n)[2:]; return (len(b)  len(b.rstrip('1')))%2 == 0


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



