A278057 - OEIS

%I #18 May 29 2024 15:14:44

%S 1,2,3,4,5,3,6,7,5,8,6,7,9,11,7,10,14,11,12,12,10,15,16,12,14,18,14,

%T 19,15,13,21,18,14,22,19,25,18,21,21,24,26,21,29,23,25,26,25,31,23,26,

%U 33,30,28,30,28,37,27,31,37,31,25,39

%N Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 5.

%C Similar to Hofstadter's Q-sequence A005185 but with different starting values.

%C Much like the Hofstadter Q-sequence, it is not known if this sequence is defined for all positive n.

%C a(n) exists for n <= 3*10^7.

%H Nathan Fox, <a href="/A278057/b278057.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.

%t a[n_] := a[n] = If[0 < n < 6, n, a[n-a[n-1]] + a[n-a[n-2]]];

%t Array[a, 100] (* _Paolo Xausa_, May 29 2024 *)

%Y Cf. A005185, A278056, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

%K nonn

%O 1,2

%A _Nathan Fox_, Nov 10 2016