A006928 a(n) = length of (n+1)st run, with initial terms 1, 2. (Formerly M0070)

1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..108.

Eric Weisstein's World of Mathematics, Kolakoski Sequence.

Formula

a(n) = A000002(n+1), n > 1.

Example

Start with [ 1,2 ]. a(1)=1, so the second run has length 1, so a(3) must be 1. a(2)=2, so the third run has length 2, so a(4) must also be 1 and a(5) must be 2. a(3)=1, so the 4th run has length 1, so a(6) must be 1; etc. - Labos Elemer

Mathematica

a = {1, 2}; Do[AppendTo[a, 1+Mod[n, 2]], {n, 2, 80}, {i, a[[n]]}]; a (* Jean-François Alcover, Aug 09 2016, adapted from PARI *)

Prog

(PARI) a=[ 1, 2 ]; for(n=2, 80, for(i=1, a[ n ], a=concat(a, 1+(n%2)))); a

Crossrefs

Essentially the same as Kolakoski sequence A000002.

Sequence in context: A086412 A192006 A378285 * A087890 A245077 A008676

Adjacent sequences: A006925 A006926 A006927 * A006929 A006930 A006931

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved