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 A005375 a(0) = 0; a(n) = n - a(a(a(a(n-1)))) for n > 0. (Formerly M0458) 4
 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)
 OFFSET 0,4 COMMENTS Rule for n-th term: a(n) = An, where An denotes the LamÃ© 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 LamÃ© 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 a(A194081(n)) = n and a(m) <> n for m < A194081(n). - Reinhard Zumkeller, Aug 17 2011 REFERENCES 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). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Nick Hobson, Python program for this sequence FORMULA 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 MAPLE H:=proc(n) option remember; if n=1 then 1 else n-H(H(H(H(n-1)))); fi; end proc; MATHEMATICA 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 *) PROG (Haskell) a005375 n = a005375_list !! n a005375_list =  0 : 1 : zipWith (-)    [2..] (map a005375 (map a005375 (map a005375 (tail a005375_list)))) -- Reinhard Zumkeller, Aug 17 2011 CROSSREFS Sequence in context: A198454 A063882 A097873 * A138370 A125051 A064067 Adjacent sequences:  A005372 A005373 A005374 * A005376 A005377 A005378 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Jul 12 2000 STATUS approved

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Last modified July 20 14:12 EDT 2019. Contains 325182 sequences. (Running on oeis4.)