A005376 a(n) = n - a(a(a(a(a(n-1))))). (Formerly M0464)

0, 1, 1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 51, 52, 52, 53, 54, 54

Offset

0,4

Comments

Conjecture: a(n) is approximately c*n, where c is the real root of x^5+x-1 = 0, c=0.754877666246692760049508896... - Benoit Cloitre, Nov 05 2002

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-5): A003520) in the Zeckendorffian expansion (obtained by repeatedly subtracting the largest Lamé number you can until nothing remains) with Lm(i-1) (A1=1). For example: 58 = 45 + 11 + 2, so a(58) = 34 + 8 + 1 = 43. - Diego Torres (torresvillarroel(AT)hotmail.com), Nov 24 2002

References

Douglas R. 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

G. C. Greubel, Table of n, a(n) for n = 0..10000

Nick Hobson, Python program for this sequence

Index entries for Hofstadter-type sequences

Index entries for sequences from "Goedel, Escher, Bach"

Maple

H:=proc(n) option remember; if n=1 then 1 else n-H(H(H(H(H(n-1))))); fi; end proc;

Mathematica

a[n_]:= a[n]= If[n<1, 0, n -a[a[a[a[a[n-1]]]]]];
Table[a[n], {n, 0, 100}] (* G. C. Greubel, Nov 16 2022 *)

Prog

(SageMath)
@CachedFunction # a = A005376
def a(n): return 0 if (n==0) else n - a(a(a(a(a(n-1)))))
[a(n) for n in range(101)] # G. C. Greubel, Nov 16 2022

Crossrefs

Cf. A005206, A005374, A005375, A100721.

Sequence in context: A317442 A132172 A080680 * A196362 A195879 A305398

Adjacent sequences: A005373 A005374 A005375 * A005377 A005378 A005379

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jul 12 2000

Status

approved