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 A130747 A self referential sequence related to Mancala solitaire (see comment). 4
 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, 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, 31, 11, 32, 6, 33, 4, 34, 12, 35, 3, 36, 2, 37, 13, 38, 7, 39, 1, 40, 14, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. - Reinhard Zumkeller, Jun 23 2009 A082447(n) = number of ones <= n. - Reinhard Zumkeller, Jul 01 2009 REFERENCES 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. S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.4.7. LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 Franklin T. Adams-Watters, Doubly Fractal Sequences and ordinal transform D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37, 51-58, 1988. P. Erdõs and E. Jabotinsky, On sequences of integers generated by a sieving process, I, Indagationes Math., 20, 115-123, 1958. P. Erdõs and E. Jabotinsky, On sequences of integers generated by a sieving process, II, Indagationes Math., 20, 124-128, 1958. MATHEMATICA max = 100; A130747 = Flatten[ Transpose[ {Range[max], Table[0, {max}]}]]; Do[ hole = Last[ Position[ A130747, 0, 1, A130747[[n]] ]]; A130747[[hole]] = A130747[[n]], {n, 1, max}]; A130747 (* Jean-François Alcover, Dec 08 2011 *) CROSSREFS Cf. A002491. Sequence in context: A078898 A246277 A260739 * A055440 A250028 A101279 Adjacent sequences:  A130744 A130745 A130746 * A130748 A130749 A130750 KEYWORD nice,nonn AUTHOR Benoit Cloitre, Jul 12 2007 STATUS approved

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)