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
From Ctibor O. Zizka, Dec 28 2024: (Start)
Numbers k >= 1 such that (k + 1)*(k + 2*r)/2 is not a square for any r >= 1.
Numbers k such that A076114(k + 1) = 0. (End)
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
(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))))
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Nadia Heninger and N. J. A. Sloane, Dec 16 2007
EXTENSIONS
More terms from Stefan Steinerberger, Dec 18 2007
STATUS
approved