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A140081 Period 4: repeat [0, 1, 1, 2]. 7
0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also fix e = 4; then a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple k*e (0 <= k <= n/e) which is a child of n.

A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.

LINKS

Table of n, a(n) for n=0..98.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

FORMULA

a(n) = (1/12)*(8*(n mod 4)-((n+1) mod 4) + 2*((n+2) mod 4) - ((n+3) mod 4)), with n >= 0. - Paolo P. Lava, Jun 06 2008

a(n) = 1 - (1/4)*(1-i)*i^n - (1/2)*(-1)^n - (1/4)*(1+i)*(-i)^n, where i=sqrt(-1), for n >= 0. - Paolo P. Lava, Jul 17 2008

a(n) = 1 + a(n - 1 - a(n-1)) + 2*a(a(n-1)) - 2*a(n-1), a(0)=0. - Ramasamy Chandramouli, Jan 31 2010

a(n) = A047624(n+2) - A047624(n+1) - 1. - Reinhard Zumkeller, Feb 21 2010

a(n) = 1 - cos(Pi*n/2)/2 - sin(Pi*n/2)/2 - (-1)^n/2. - R. J. Mathar, Oct 08 2011

a(n) = ((n mod 4) + (n mod 2))/2. - Gary Detlefs, Apr 21 2012

From Colin Barker, Jan 13 2013: (Start)

a(n) = a(n-4).

G.f.: -x*(2*x^2+x+1) / ((x-1)*(x+1)*(x^2+1)). (End)

a(n) = floor((3*(n mod 4) + 1)/4). - Wesley Ivan Hurt, Mar 27 2014

From Wesley Ivan Hurt, Apr 22 2015: (Start)

a(n) = floor(1/2 + (n mod 4)/2).

a(n) = 1 - (-1)^n/2 - (-1)^(n/2 - 1/4 + (-1)^n/4)/2. (End)

a(n) = n - floor(n/2) - 2*floor(n/4). - Ridouane Oudra, Oct 30 2019

MAPLE

A140081:=n->floor((3*(n mod 4)+1)/4); seq(A140081(n), n=0..100); # Wesley Ivan Hurt, Mar 27 2014

MATHEMATICA

PadLeft[{}, 100, {0, 1, 1, 2}] (* Harvey P. Dale, Aug 19 2011 *)

Table[Floor[(3 Mod[n, 4] + 1)/4], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 27 2014 *)

PROG

See link in A140080 for Fortran program.

(PARI) a(n)=n%4-n%4\2 \\ Jaume Oliver Lafont, Aug 28 2009

(Haskell)

a140081 n = div (mod n 4 + mod n 2) 2

a140081_list = cycle [0, 1, 1, 2]  -- Reinhard Zumkeller, Aug 15 2015

CROSSREFS

Cf. A140201. - Reinhard Zumkeller, Feb 21 2010

Sequence in context: A276771 A062984 A105243 * A280596 A112345 A336469

Adjacent sequences:  A140078 A140079 A140080 * A140082 A140083 A140084

KEYWORD

nonn,easy

AUTHOR

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

STATUS

approved

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Last modified December 1 16:28 EST 2021. Contains 349430 sequences. (Running on oeis4.)