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Search: id:A089242
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| A089242 |
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Sequence is S(infinity), where S(1) = 1, S(m+1) = concatenation S(m), a(m)+1, S(m) and a(m) is the m-th term of S(m). a(m) is also the m-th term of the sequence. |
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| 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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S(m) has 2^m - 1 elements and is palindromic for all m.
First occurrence of k: 1,2,4,16,65536,...,. A014221: a(n+1) = 2^a(n). This is an Ackermann function. - Robert G. Wilson v May 30 2006.
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..65536
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FORMULA
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a(m) = number of c's such that 0 = c(c(c(c(...c(m)...)))), where 2^c(n) is the highest power of 2 which divides evenly into n (i.e. a(m) = 1 + a(c(m))); also c(m) = A007814(m).
In other words, a(n) = number of iterates of A007814 until a zero is encountered.
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MATHEMATICA
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c[n_] := (i++; Block[{k = 0, m = n}, While[ EvenQ[m], k++; m /= 2]; k]); f[n_] := (i = 0; NestWhile[c, n, # >= 1 &]; i); Array[f, 105] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 30 2006)
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CROSSREFS
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Cf. A007814.
Adjacent sequences: A089239 A089240 A089241 this_sequence A089243 A089244 A089245
Sequence in context: A078734 A028293 A092782 this_sequence A029423 A059130 A094959
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KEYWORD
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nonn,easy
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Dec 13 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 31 2005
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