

A121539


Numbers n such that the binary expansion of n ends in an even number of 1's.


22



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
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OFFSET

1,2


COMMENTS

Equivalently, increasing sequence defined by: "if n appears a*n+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 member.
Consists of all even numbers together with A131323.
A035263(a(n)) = 1. [Reinhard Zumkeller, Mar 01 2012]


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Narad Rampersad, Manon Stipulanti, The Formal Inverse of the PeriodDoubling Sequence, arXiv:1807.11899 [math.CO], 2018.


FORMULA

A010060(a(n)) + A010060(a(n)+1) = 1. [Vladimir Shevelev, Jun 16 2009]
a(n) = A003159(n)  1. [Reinhard Zumkeller, Mar 01 2012]
a(n) = 1.5n + O(log n).  Charles R Greathouse IV, Sep 23 2012


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
 Reinhard Zumkeller, Mar 01 2012
(PARI) is(n)=valuation(n+1, 2)%2==0 \\ Charles R Greathouse IV, Sep 23 2012
(MAGMA) [n: n in [0..200]  Valuation(n+1, 2) mod 2 eq 0 ]; // Vincenzo Librandi, Apr 16 2015


CROSSREFS

Cf. A121538, A121540, A121541, A121542.
Sequence in context: A097274 A322572 A254438 * A257457 A122138 A047418
Adjacent sequences: A121536 A121537 A121538 * A121540 A121541 A121542


KEYWORD

nonn,easy


AUTHOR

Zak Seidov, Aug 08 2006


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Dec 17 2007


STATUS

approved



