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A131323
Odd numbers whose binary expansion ends in an even number of 1's.
22
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
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
(Python)
from itertools import count, islice
def A131323_gen(startvalue=3): # generator of terms >= startvalue
return map(lambda n:(n<<1)+1, filter(lambda n:(~(n+1)&n).bit_length()&1, count(max(startvalue>>1, 1))))
A131323_list = list(islice(A131323_gen(), 30)) # Chai Wah Wu, Sep 11 2024
CROSSREFS
Sequence in context: A044971 A106374 A075330 * A050592 A032466 A060698
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Stefan Steinerberger, Dec 18 2007
STATUS
approved