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A043545
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(Maximal base-2 digit of n) - (minimal base-2 digit of n).
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12
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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
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OFFSET
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0,1
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COMMENTS
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Characteristic function of A062289 (non-Mersenne numbers A000225). - Omar E. Pol, Sep 05 2021
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LINKS
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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.
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FORMULA
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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
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EXAMPLE
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G.f. = x^2 + x^4 + x^5 + x^6 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + ...
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MATHEMATICA
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mb2d[n_]:=Module[{n2=IntegerDigits[n, 2]}, Max[n2]-Min[n2]]; Array[mb2d, 120, 0] (* Harvey P. Dale, Feb 24 2015 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, n++; n != 2^valuation(n, 2))}; /* Michael Somos, Aug 25 2003 */
(Haskell)
a043545 = (1 -) . a036987 -- Reinhard Zumkeller, Nov 02 2013
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CROSSREFS
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Cf. A000225, A036987, A062289.
Column k=0 of A347519.
Sequence in context: A353670 A252744 A340373 * A094754 A321694 A262684
Adjacent sequences: A043542 A043543 A043544 * A043546 A043547 A043548
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KEYWORD
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nonn,base
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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