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A005375
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a(0) = 0; a(n) = n - a(a(a(a(n-1)))) for n > 0.
(Formerly M0458)
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5
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0, 1, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 37, 37, 38, 39, 40, 41, 41, 42, 42, 43, 44, 44, 45, 46, 47, 47, 48, 49, 50, 51, 51, 52, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Rule for n-th term: a(n) = An, where An denotes the Lamé antecedent to (or right shift of) n, which is found by replacing each Lm(i) (Lm(n) = Lm(n-1) + Lm(n-4): A003269) in the Zeckendorffian expansion (obtained by repeatedly subtracting the largest Lamé number you can until nothing remains) by Lm(i-1) (A1=1). For example: 58 = 50 + 7 + 1, so a(58)= 36 + 5 + 1 = 42. - Diego Torres (torresvillarroel(AT)hotmail.com), Nov 24 2002
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REFERENCES
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D. Hofstadter, "Goedel, Escher, Bach", p. 137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Conjecture: a(n) = floor(c*n) + 0 or 1, where c is the positive real root of x^4+x-1 = 0, c=0.724491959000515611588372282... - Benoit Cloitre, Nov 05 2002
Note: in the previous conjecture, the 0 or 1 difference could actually be between -1 and 2, see for instance a(120)=88 for a difference of 2 and a(243)=175 for a difference of -1. - Pierre Letouzey, Jul 11 2018
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MAPLE
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H:=proc(n) option remember; if n=1 then 1 else n-H(H(H(H(n-1)))); fi; end proc;
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MATHEMATICA
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a[0]:= 0; a[n_]:= a[n]= a[n] = n - a[a[a[a[n-1]]]]; Table[a[n], {n, 0, 73}] (* Alonso del Arte, Aug 17 2011 *)
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PROG
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(Haskell)
a005375 n = a005375_list !! n
a005375_list = 0 : 1 : zipWith (-)
[2..] (map a005375 (map a005375 (map a005375 (tail a005375_list))))
(SageMath)
def a(n): return 0 if (n==0) else n - a(a(a(a(n-1))))
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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