OFFSET
0,1
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Paul Barry, Conjectures and results on some generalized Rueppel sequences, arXiv:2107.00442 [math.CO], 2021.
FORMULA
0 followed by a string of 2^k - 1 1's. Also a(n)=0 iff n = 2^m - 1.
G.f.: 1/(1-x) - Sum_{k>=0} x^(2^k-1). - Michael Somos, Aug 25 2003
a(n) = 1 - A036987(n). 1's complement of Fredhold-Rueppel sequence. - Michael Somos, Aug 25 2003
a(n) = (1 + (-1)^binomial(n, floor(n/2)))/2. - Paul Barry, Jun 07 2006
Ignoring first zero and beginning instead with offset 2, a(n) = A006530(n) mod 2. - Rick L. Shepherd, Jun 09 2008
a(n) = A000777(n) mod 2, for n > 0. - John M. Campbell, Jul 16 2016
EXAMPLE
G.f. = x^2 + x^4 + x^5 + x^6 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + ...
MATHEMATICA
mb2d[n_]:=Module[{n2=IntegerDigits[n, 2]}, Max[n2]-Min[n2]]; Array[mb2d, 120, 0] (* Harvey P. Dale, Feb 24 2015 *)
PROG
(PARI) {a(n) = if( n<0, 0, n++; n != 2^valuation(n, 2))}; /* Michael Somos, Aug 25 2003 */
(PARI) a(n) = !!bitand(n, n+1); \\ Ruud H.G. van Tol, Sep 12 2023
(Haskell)
a043545 = (1 -) . a036987 -- Reinhard Zumkeller, Nov 02 2013
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved