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Search: id:A134680
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| A134680 |
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a(n) = length of the Meta-Fibonacci sequence f(1) = ... = f(n) = 1; f(k)=f(k-f(k-1))+f(k-f(k-n)), if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite. |
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+0
1
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| 6, 0, 164, 0, 60, 2354, 282, 1336, 100, 1254, 366, 419, 498, 483, 778, 1204, 292, 373, 845, 838, 1118, 2120, 815, 2616, 686, 1195, 745, 1112, 2132, 1588, 754, 1227, 1279, 1661, 716, 2275, 784, 2341, 1874, 1463, 1122, 2800, 1350, 1613, 2279, 1557, 1532
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Such a sequence has finite length when the k-th term becomes greater than k.
The term a(2) = 0 is only conjectural - see A005185. - N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
Index entries for Hofstadter-type sequences
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EXAMPLE
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a(1) = 6: the f-sequence is defined by f(1) = 1, f(n) = 2f(n-f(n-1)), which gives 1,2,2,4,2,8 but f(7) = 2f(-1) is undefined, so the length is 6.
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MATHEMATICA
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Table[Clear[a]; a[n_] := a[n] = If[n<=k, 1, a[n-a[n-1]]+a[n-a[n-k]]]; t={1}; n=2; While[n<10000 && a[n-1]<n, AppendTo[t, a[n]]; n++ ]; len=Length[t]; If[len==9999, 0, len], {k, 100}]
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CROSSREFS
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Cf. A005185, A046700, A063882, A132172, A134679 (sequences for n=2..6).
Sequence in context: A005212 A167028 A052679 this_sequence A111372 A156444 A122192
Adjacent sequences: A134677 A134678 A134679 this_sequence A134681 A134682 A134683
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 06 2007
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