A205883 -id:A205883

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A205600

Start with first run [1,2] then, for n >= 2, the n-th run is a(n) times [a(1),...,a(n-1)].

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

What is the density of 1's in the sequence (it seems it is >0.7 see A206767 )? The length of the n-th run also appears to behave like c*n^2 with c=0.64...(see A205883).

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

First run is given by 12 so a(2)=2 and the second run is 2 times a(1)=1 and we get 1211. Next a(3)=1 hence the third run is 1 time [a(1),a(2)]=12 and we get 121112. a(4)=1 hence 4th run is 1 time 121 and we get 121112121 etc.

PROG

(PARI) /* compute 6555 terms: */

v=[1, 2]; for(n=2, 100, v=if(v[n]-2, concat(v, vector(n-1, i, v[i])), concat(concat(v, vector(n-1, i, v[i])), vector(n-1, i, v[i])))); a(n)=v[n]

CROSSREFS

Cf. A205883, A206767.

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 10 2013

STATUS

approved

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