

A005375


a(0) = 0; a(n) = n  a(a(a(a(n1)))) 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
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OFFSET

0,4


COMMENTS

Rule for nth 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(n1) + Lm(n4): A003269) in the Zeckendorffian expansion (obtained by repeatedly subtracting the largest LamÃ© number you can until nothing remains) by Lm(i1) (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
Index entries for Hofstadtertype sequences
Index entries for sequences from "Goedel, Escher, Bach"


FORMULA

Conjecture: a(n) = floor(c*n) + 0 or 1, where c is the positive real root of x^4+x1 = 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 nH(H(H(H(n1)))); 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

N. J. A. Sloane


EXTENSIONS

More terms from James A. Sellers, Jul 12 2000


STATUS

approved



