A106733 a(n) = a(a(a(a(n - a(n-1))))) + a(n - a(n-2)) with a(1) = a(2) = 1.

1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 9, 8, 9, 9, 9, 9, 9, 9, 9, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 16, 17, 17, 17, 17

Offset

1,3

Comments

A fifth-order recursion based on Hofstadter's Q-sequence A005185.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Formula

a(n) = a(a(a(a(n - a(n-1))))) + a(n - a(n-2)) with a(1) = a(2) = 1.

Mathematica

Hofstadter1[1] = Hofstadter1[2] = 1; Hofstadter1[n_Integer?Positive] := Hofstadter1[n] = Hofstadter1[Hofstadter1[Hofstadter1[Hofstadter1[n - Hofstadter1[n - 1]]]]] + Hofstadter1[ n - Hofstadter1[n - 2]]; a = Table[Hofstadter1[n], {n, 1, digits}]

Prog

(Sage)
@CachedFunction
def a(n): return 1 if (n<3) else a(a(a(a(n -a(n-1))))) + a(n-a(n-2));
[a(n) for n in (1..90)] # G. C. Greubel, Sep 11 2021

Crossrefs

Cf. A005185, A087842.

Sequence in context: A209869 A087839 A106742 * A087838 A057627 A013940

Adjacent sequences: A106730 A106731 A106732 * A106734 A106735 A106736

Keyword

nonn,easy

Author

Roger L. Bagula, May 30 2005

Status

approved