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A038219 The Ehrenfeucht-Mycielski sequence (0,1-version): a maximally unpredictable sequence. 11
0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Comment from Christopher Carl Heckman, Feb 10 2005: The sequence starts 0,1,0 and continues according to the following rule: find the longest sequence at the end that has occurred at least once previously. If there are more than one previous occurrences select the last one. The next digit of the sequence is the opposite of the one following the previous occurrence.

REFERENCES

A. Ehrenfeucht and J. Mycielski, A pseudorandom sequence - how random is it?, Amer. Math. Monthly, 99 (1992), 373-375.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..5000

Terry McConnell, The Ehrenfeucht-Mycielski Sequence

K. Sutner, The Ehrenfeucht-Mycielski sequence, 2001

K. Sutner, The Ehrenfeucht-Mycielski sequence, 2001 [Cached copy]

PROG

(Haskell)

a038219 n = a038219_list !! n

a038219_list = 0 : f [0] where

   f us = a' : f (us ++ [a']) where

        a' = b $ reverse $ map (`splitAt` us) [0..length us - 1] where

           b ((xs, ys):xyss) | vs `isSuffixOf` xs = 1 - head ys

                            | otherwise          = b xyss

        vs = fromJust $ find (`isInfixOf` init us) $ tails us

-- Reinhard Zumkeller, Dec 05 2011

CROSSREFS

Cf. A007061 (1, 2 version).

Cf. A201881 (run lengths).

Cf. also A253059, A253060, A253061.

Sequence in context: A189572 A244735 A245938 * A172486 A189668 A215530

Adjacent sequences:  A038216 A038217 A038218 * A038220 A038221 A038222

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Joshua Zucker, Aug 11 2006

Offset changed by Reinhard Zumkeller, Dec 11 2011

STATUS

approved

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Last modified March 1 11:54 EST 2015. Contains 255112 sequences.