login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007782 Number of factors in the infinite word formed by the Kolakoski sequence A000002. 3

%I

%S 1,2,4,6,10,14,18,26,34,42,50,62,78,94,110,126,142,162,186,218,250,

%T 282,314,346,378,410,446,486,534,590,654,718,782,846,910,974,1038,

%U 1102,1166,1234,1302,1378,1458,1554,1658,1774,1898,2026,2154,2282,2410,2538,2666

%N Number of factors in the infinite word formed by the Kolakoski sequence A000002.

%C a(n) = number of different substrings of length n found in Kolakoski sequence A000002. It is conjectured that a(n) grows like n^(log(3)/log(3/2)).

%D M. Dekking: "What is the long range order in the Kolakoski sequence?" in: The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer, Dordrecht (1997), pp. 115-125.

%H D. Wilson, <a href="/A007782/b007782.txt">Table of n, a(n) for n = 0..100</a>.

%e For length 3 only the strings 112, 121, 211, 221, 212, 122 occur, so a(3) = 6. For length 4 only the 10 strings 1121, 1122, 1211, 1212, 1221, 2112, 2121, 2122, 2211, 2212 occur.

%t nMax = 52; A007782[m_] := A007782[m] = (kolak = {1, 2, 2}; For[n = 3, n <= m, n++, For[k = 1, k <= kolak[[n]], k++, AppendTo[ kolak, 1 + Mod[n - 1, 2]]]]; factors[n_] := Table[ kolak[[k ;; k + n - 1]], {k, 1, Length[kolak] - n + 1}]; Table[ factors[n] // Union // Length, {n, 0, nMax}]); A007782[nMax]; A007782[m = 2*nMax]; While[ A007782[m] != A007782[m/2], m = 2*m]; A007782[m] (* _Jean-François Alcover_, Jul 24 2013 *)

%Y Cf. A000002.

%K nonn,nice

%O 0,2

%A Patricia Lamas (lamas(AT)math.uqam.ca)

%E Additional comments from Michael Baake (mbaake(AT)pion09.tphys.physik.uni-tuebingen.de), Feb 19, 2001.

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 December 1 20:25 EST 2021. Contains 349435 sequences. (Running on oeis4.)