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A043545 (Maximal base-2 digit of n) - (minimal base-2 digit of n). 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Characteristic function of A062289 (non-Mersenne numbers A000225). - Omar E. Pol, Sep 05 2021
LINKS
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
Column k=0 of A347519.
Sequence in context: A353670 A252744 A340373 * A094754 A321694 A262684
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified December 11 15:11 EST 2023. Contains 367727 sequences. (Running on oeis4.)