A043545 (Maximal base-2 digit of n) - (minimal base-2 digit of n).
0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 0
Examples
G.f. = x^2 + x^4 + x^5 + x^6 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + ...
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.
Programs
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Haskell
a043545 = (1 -) . a036987 -- Reinhard Zumkeller, Nov 02 2013
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Mathematica
mb2d[n_]:=Module[{n2=IntegerDigits[n,2]},Max[n2]-Min[n2]]; Array[mb2d,120,0] (* Harvey P. Dale, Feb 24 2015 *) -
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
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
Comments