A131323 Odd numbers whose binary expansion ends in an even number of 1's.

3, 11, 15, 19, 27, 35, 43, 47, 51, 59, 63, 67, 75, 79, 83, 91, 99, 107, 111, 115, 123, 131, 139, 143, 147, 155, 163, 171, 175, 179, 187, 191, 195, 203, 207, 211, 219, 227, 235, 239, 243, 251, 255, 259, 267, 271, 275, 283, 291, 299, 303, 307, 315, 319, 323, 331

Offset

1,1

Comments

Also numbers of the form (4^a)*b - 1 with positive integer a and odd integer b. The sequence has linear growth and the limit of a(n)/n is 6. - Stefan Steinerberger, Dec 18 2007

Evil and odious terms alternate. - Vladimir Shevelev, Jun 22 2009

Also odd numbers of the form m = (A079523(k)-1)/2. - Vladimir Shevelev, Jul 06 2009

As a set, this is the complement of A079523 in the odd numbers. - Michel Dekking, Feb 13 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Thomas Zaslavsky, Anti-Fibonacci Numbers: A Formula, Sep 26 2016

Formula

a(n) = 2*A079523(n) + 1. - Michel Dekking, Feb 13 2019

Example

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

Maple

N:= 1000: # to get all terms up to N
Odds:= [seq(2*i+1, i=0..floor((N-1)/2)]:
f:= proc(n) local L, x;
   L:= convert(n, base, 2);
   x:= ListTools:-Search(0, L);
   if x = 0 then type(nops(L), even) else type(x, odd) fi
end proc:
A131323:= select(f, Odds); # Robert Israel, Apr 02 2014

Mathematica

Select[Range[500], OddQ[ # ] && EvenQ[FactorInteger[ # + 1][[1, 2]]] &] (* Stefan Steinerberger, Dec 18 2007 *)
en1Q[n_]:=Module[{ll=Last[Split[IntegerDigits[n, 2]]]}, Union[ll] =={1} &&EvenQ[Length[ll]]]; Select[Range[1, 501, 2], en1Q] (* Harvey P. Dale, May 18 2011 *)

Prog

(PARI) is(n)=n%2 && valuation(n+1, 2)%2==0 \\ Charles R Greathouse IV, Aug 20 2013

Crossrefs

Cf. A079523, A121539.

Sequence in context: A044971 A106374 A075330 * A050592 A032466 A060698

Adjacent sequences: A131320 A131321 A131322 * A131324 A131325 A131326

Keyword

nonn,easy

Author

Nadia Heninger and N. J. A. Sloane, Dec 16 2007

Extensions

More terms from Stefan Steinerberger, Dec 18 2007

Status

approved