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Relative of Hofstadter Q-sequence: a(1) = 57, a(2) = 2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
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%I #9 May 31 2024 05:48:14

%S 57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,

%T 2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,57,2,

%U 57,2,57,59,2,116,2,116,2,116,2,116,2,116,2,116,2,116

%N Relative of Hofstadter Q-sequence: a(1) = 57, a(2) = 2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

%C In calculating terms of this sequence, use the convention that a(n)=0 for n<=0.

%C This sequence is eventually, beginning with a(3128), quasilinear with quasiperiod 1402.

%H Nathan Fox, <a href="/A278068/b278068.txt">Table of n, a(n) for n = 1..10000</a>

%H Nathan Fox, <a href="https://vimeo.com/191094180">Hofstadter-like Sequences over Nonstandard Integers"</a>, Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.

%H Nathan Fox, <a href="/A278068/a278068.txt">Formula for a(n)</a>

%t a[1] = 57; a[2] = 2; a[n_] := a[n] = If[n < 1, 0, a[n-a[n-1]] + a[n-a[n-2]]];

%t Array[a, 100] (* _Paolo Xausa_, May 31 2024 *)

%Y Cf. A005185, A275163, A278066, A278067.

%K nonn

%O 1,1

%A _Nathan Fox_, Nov 13 2016