1,3

To built the sequence, start from:

1,_,2,_,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...

At n-th step use the rule: " fill a(n)-th hole with a(n) " (holes are numbered from 1 at each step)

So step 1 is "fill first hole with 1" giving:

1,1,2,_,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...

Since a(2)=1 step 2 is still "fill first hole with 1" giving:

1,1,2,1,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...

Since a(3)=2 step 3 is "fill second hole with 2" giving:

1,1,2,1,3,_,4,2,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...

Since a(4)=1 step 4 is "fill first hole with 1" giving:

1,1,2,1,3,1,4,2,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...

Since a(5)=3 step 5 is "fill third hole with 3" giving:

1,1,2,1,3,1,4,2,5,_,6,_,7,3,8,_,9,_,10,_,11,_,12,_,...

Iterating the process indefinitely yields:

1,1,2,1,3,1,4,2,5,1,6,1,7,3,8,2,9,1,10,4,11,1,12,2,13,5,..

Indices where 1's occur are given by n=1,2,4,6,10,... which are the smallest number of stones in Mancala solitaire which make use of n-th hole. If f(k) denotes this sequence k^2/f(k)-->pi as k-->infty.

Ordinal transform of A028920 - Benoit Cloitre, Aug 03 2007

Although A028920 and A130747 are not fractal sequences (according to Kimberling's definition) we say they are "mutual fractal sequences" since the ordinal transform of one gives the other. - Benoit Cloitre, Aug 03 2007

a(A002491(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 23 2009]

A082447(n) = number of ones <= n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 01 2009]

D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37,51-58,1988.

B. Cloitre, Pi in a hole, in preparation, 2007

Y. David, On a sequence generated by a sieving process, Riveon Lematematika,11(1957), 26-31.

P. Erdos and E. Jabotinsky, On a sequence of integers ..., Indagationes Math., 20,115-128, 1958.

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.4.7.

R. Zumkeller, Table of n, a(n) for n = 1..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 23 2009]

Franklin T. Adams-Watters, Doubly Fractal Sequences and ordinal transform

Cf. A002491.

Sequence in context: A029207 A111902 A078898 this_sequence A055440 A101279 A064576

Adjacent sequences: A130744 A130745 A130746 this_sequence A130748 A130749 A130750

nice,nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 12 2007