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A106733
a(n) = a(a(a(a(n - a(n-1))))) + a(n - a(n-2)) with a(1) = a(2) = 1.
2
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
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
Sequence in context: A209869 A087839 A106742 * A087838 A057627 A013940
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 30 2005
STATUS
approved