OFFSET
1,2
COMMENTS
Either of form 2a(m) or 4k+1, k >= 0, 0 < m < n.
a(n) such that A038189(a(n)) = 0.
Numbers n such that kronecker(n, m) = kronecker(m, n) for all m. - Michael Somos, Sep 24 2005
The Dragon curve A014577 (but changing the offset to 1): (1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...) = the characteristic function of A091072. - Gary W. Adamson, Apr 11 2010
Also indices of 1 in A034947. - Jianing Song, Apr 24 2021
The terms in the sequence are the same as the terms in the odd columns of the table in A135764 with headings 4k+1: (1, 5, 9, 13...). A014577(n) = 1 if n is in that set, but A014577(n) = 0 if n is in the set of even columns in the A135764 table. - Gary W. Adamson, May 29 2021
The asymptotic density of this sequence is 1/2. - Amiram Eldar, Sep 14 2024
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J.-P. Allouche and J. Shallit, On three conjectures of P. Barry, arxiv preprint arXiv:2006.04708 [math.NT], June 8 2020.
Paul Barry, Some observations on the Rueppel sequence and associated Hankel determinants, arXiv:2005.04066 [math.CO], 2020.
Kevin Ryde, Iterations of the Dragon Curve, see index TurnLeft, with a(n) = TurnLeft(n-1).
J. E. S. Socolar and J. M. Taylor, An aperiodic hexagonal tile, arXiv:1003.4279 [math.CO], 2010.
FORMULA
A014707(a(n) + 1) = 0. - Reinhard Zumkeller, Sep 28 2011
A055975(a(n)) > 0. - Reinhard Zumkeller, Apr 28 2012
EXAMPLE
x + 2*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 9*x^6 + 10*x^7 + 13*x^8 + 16*x^9 + ...
MATHEMATICA
Select[ Range[129], EvenQ[ (#/2^IntegerExponent[#, 2] - 1)/2 ] & ] (* Jean-François Alcover, Feb 16 2012, after Pari *)
PROG
(PARI) for(n=1, 200, if(((n/2^valuation(n, 2)-1)/2)%2==0, print1(n", ")))
(PARI) {a(n) = local(m, c); if( n<1, 0, c=1; m=1; while( c<n, m++; if( ((m / 2^valuation( m, 2) - 1) / 2)%2==0, c++)); m)} /* Michael Somos, Sep 24 2005 */
(PARI) a(n) = if(n=2*n-2, my(t=1); forstep(i=logint(n, 2), 0, -1, if(bittest(n, i)==t, n--; t=!t))); n+1; \\ Kevin Ryde, Mar 21 2021
(Haskell)
import Data.List (elemIndices)
a091072 n = a091072_list !! (n-1)
a091072_list = map (+ 1) $ elemIndices 0 a014707_list
-- Reinhard Zumkeller, Sep 28 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Feb 22 2004
STATUS
approved