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A008351
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Concatenate a(n-1) and a(n-2).
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3
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1, 2, 21, 212, 21221, 21221212, 2122121221221, 212212122122121221212, 2122121221221212212122122121221221, 2122121221221212212122122121221221212212122122121221212
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A "non-commutative Fibonacci" sequence. Often written as: a, b, ba, bab, babba, babbabab, babbababbabba, babbababbabbababbabab, ...
Converges in the appropriate topology. - Dylan Thurston, Jan 28 2005
Do a web search on babbababbabbababbabab to get further links.
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REFERENCES
| D. E. Knuth, "The Art of Programming", Volume 1, "Fundamental Algorithms", third edition, problem 36 on page 86.
K. B. Stolarsky, Canadian Math. Bull. 19 (1976) pp. 473-482.
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LINKS
| Wikipedia, Lindenmayer system
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FORMULA
| a(n)=a(n-1)*10^floor{log10[a(n-2)]+1}+a(n-2), with a(1)=1, a(2)=2. [From Paolo P. Lava (paoloplava(AT)gmail.com), Mar 05 2010]
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MATHEMATICA
| a[1] = 1; a[2] = 2; a[n_] := 10^Floor[ Log[10, a[n - 2]] +1]*a[n - 1] + a[n - 2] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 26 2006)
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CROSSREFS
| See A008352 for another version.
Cf. A014675: 1->2, 2->21.
Sequence in context: A037495 A024763 A037575 * A037743 A037638 A131698
Adjacent sequences: A008348 A008349 A008350 * A008352 A008353 A008354
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KEYWORD
| nonn,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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