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Search: id:A093878
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| A093878 |
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a(1)=a(2)=1; for n >=3, a(n) = a(a(a(n-1))) + a(n-a(a(n-1))). |
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+0
9
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| 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 31, 32, 33, 33, 33, 33, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 47, 47, 48, 48
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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For n>1: a(n)<n*(phi-1) iff n is in A001519 where phi is the golden ratio = (1+sqrt(5))/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 27 2004
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REFERENCES
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J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
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FORMULA
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a(A001519(n)) = floor((phi-1)*A001519(n)); a(A000045(n)) = A000045(n-1); liminf a(n)/n = phi-1; limsup a(n)/n = ? - Benoit Cloitre (benoit7848c(AT)orange.fr), May 27 2004
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MATHEMATICA
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a[1] = a[2] = 1; a[n_] := a[n] = a[a[a[n - 1]]] + a[n - a[a[n - 1]]]; Table[ a[n], {n, 75}] (from Robert G. Wilson v May 27 2004)
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PROGRAM
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(PARI) {m=75; v=vector(m, j, 1); for(n=3, m, a=v[v[v[n-1]]]+v[n-v[v[n-1]]]; v[n]=a); for(j=1, m, print1(v[j], ", "))} (Klaus Brockhaus)
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CROSSREFS
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Sequence in context: A074065 A024811 A131138 this_sequence A156689 A004396 A131737
Adjacent sequences: A093875 A093876 A093877 this_sequence A093879 A093880 A093881
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 27 2004
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Robert G. Wilson v (rgwv(AT)rgwv.com) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 27 2004
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