A106733 - OEIS

%I #14 Sep 11 2021 15:18:39

%S 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,

%T 9,9,9,11,10,11,11,11,11,11,11,11,11,11,13,12,13,13,13,13,13,13,13,13,

%U 13,13,13,15,14,15,15,15,15,15,15,15,15,15,15,15,15,15,17,16,17,17,17,17

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

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

%H Paolo P. Lava, <a href="/A106733/b106733.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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}]

%o (Sage)

%o @CachedFunction

%o def a(n): return 1 if (n<3) else a(a(a(a(n -a(n-1))))) + a(n-a(n-2));

%o [a(n) for n in (1..90)] # _G. C. Greubel_, Sep 11 2021

%Y Cf. A005185, A087842.

%K nonn,easy

%O 1,3

%A _Roger L. Bagula_, May 30 2005