Search: id:A130747
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%I A130747
%S A130747 1,1,2,1,3,1,4,2,5,1,6,1,7,3,8,2,9,1,10,4,11,1,12,2,13,5,14,3,15,1,16,
               6,
%T A130747 17,1,18,2,19,7,20,4,21,1,22,8,23,3,24,1,25,9,26,5,27,2,28,10,29,1,30,
               1,
%U A130747 31,11,32,6,33,4,34,12,35,3,36,2,37,13,38,7,39,1,40,14,41
%N A130747 A self referential sequence related to Mancala solitaire (see comment).
%C A130747 To built the sequence, start from:
%C A130747 1,_,2,_,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...
%C A130747 At n-th step use the rule: " fill a(n)-th hole with a(n) " (holes are 
               numbered from 1 at each step)
%C A130747 So step 1 is "fill first hole with 1" giving:
%C A130747 1,1,2,_,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...
%C A130747 Since a(2)=1 step 2 is still "fill first hole with 1" giving:
%C A130747 1,1,2,1,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...
%C A130747 Since a(3)=2 step 3 is "fill second hole with 2" giving:
%C A130747 1,1,2,1,3,_,4,2,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...
%C A130747 Since a(4)=1 step 4 is "fill first hole with 1" giving:
%C A130747 1,1,2,1,3,1,4,2,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,...
%C A130747 Since a(5)=3 step 5 is "fill third hole with 3" giving:
%C A130747 1,1,2,1,3,1,4,2,5,_,6,_,7,3,8,_,9,_,10,_,11,_,12,_,...
%C A130747 Iterating the process indefinitely yields:
%C A130747 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,..
%C A130747 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.
%C A130747 Ordinal transform of A028920 - Benoit Cloitre, Aug 03 2007
%C A130747 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
%C A130747 a(A002491(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 23 2009]
%C A130747 A082447(n) = number of ones <= n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 01 2009]
%D A130747 D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete 
               Math., 37,51-58,1988.
%D A130747 B. Cloitre, Pi in a hole, in preparation, 2007
%D A130747 Y. David, On a sequence generated by a sieving process, Riveon Lematematika,
               11(1957), 26-31.
%D A130747 P. Erdos and E. Jabotinsky, On a sequence of integers ..., Indagationes 
               Math., 20,115-128, 1958.
%D A130747 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.4.7.
%H A130747 R. Zumkeller, <a href="b130747.txt">Table of n, a(n) for n = 1..10000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 
               23 2009]
%H A130747 Franklin T. Adams-Watters, <a href="a002260.txt">Doubly Fractal Sequences 
               and ordinal transform</a>
%Y A130747 Cf. A002491.
%Y A130747 Sequence in context: A029207 A111902 A078898 this_sequence A055440 A101279 
               A064576
%Y A130747 Adjacent sequences: A130744 A130745 A130746 this_sequence A130748 A130749 
               A130750
%K A130747 nice,nonn
%O A130747 1,3
%A A130747 Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 12 2007

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