login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003324 A nonrepetitive sequence.
(Formerly M0443)
1
1, 2, 3, 4, 1, 4, 3, 2, 1, 2, 3, 2, 1, 4, 3, 4, 1, 2, 3, 4, 1, 4, 3, 4, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4, 1, 4, 3, 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4, 1, 4, 3, 4, 1, 2, 3, 2, 1, 4, 3, 4, 1, 2, 3, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let b(0) be the sequence 1,2,3,4. Proceeding by induction, let b(n) be a sequence of length 2^(n+2). Quarter b(n) into four blocks, A,B,C,D each of length 2^n, so that b(n) = ABCD. Then b(n+1) = ABCDADCB. [After Dean paper.] - Sean A. Irvine, Apr 20 2015

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Richard A. Dean, A sequence without repeats on x, x^{-1}, y, y^{-1}, Amer. Math. Monthly 72, 1965. pp. 383-385. MR 31 #350.

Françoise Dejean, Sur un Theoreme de Thue, J. Combinatorial Theory, vol. 13 A, iss. 1 (1972) 90-99.

N. J. A. Sloane, P. Flor, L. F. Meyers, G. A. Hedlund. M. Gardner, Collection of documents and notes related to A1285, A3270, A3324

MATHEMATICA

b[0] = Range[4];

b[n_] := b[n] = Module[{aa, bb, cc, dd}, {aa, bb, cc, dd} = Partition[b[n - 1], 2^(n-1)]; Join[aa, bb, cc, dd, aa, dd, cc, bb] // Flatten];

b[5] (* Jean-François Alcover, Sep 27 2017 *)

CROSSREFS

Sequence in context: A270313 A327464 A318308 * A110630 A238883 A325242

Adjacent sequences:  A003321 A003322 A003323 * A003325 A003326 A003327

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)