A274055 - OEIS

%I #40 Nov 14 2016 10:29:08

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,3,43,44,5,45,6,7,46,

%U 48,10,8,48,52,12,49,14,54,11,53,57,16,13,17,15,56,20,20

%N Relative of Hofstadter Q-sequence: a(n) = n for 1 <= n <= 42; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 42.

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

%C This sequence eventually settles into a pattern resembling A272610.

%H Nathan Fox, <a href="/A274055/b274055.txt">Table of n, a(n) for n = 1..40000</a>

%H N. 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.

%F If the index is between 77 and 89 (inclusive), then a(5n) = 3, a(5n+1) = 5, a(5n+2) = 88n-1188, a(5n+3) = 5, a(5n+4) = 88.

%F If the index is between 95 and 397 (inclusive), then a(5n) = 396n-6820, a(5n+1) = 3, a(5n+2) = 396, a(5n+3) = 3, a(5n+4) = 5.

%F If the index is between 403 and 24860 (inclusive), then a(5n) = 24860, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 24860n-1939476, a(5n+4) = 5.

%F If the index is at least 24863, then a(5n) = 24860*A272613(n-4972), a(5n+1) = 4, a(5n+2) = 5*A272611(n-4972), a(5n+3) = 5*A272611(n-4971), a(5n+4) = 5*A272612(n-4971). This pattern lasts as long as A272611 exists (which is conjectured to be forever).

%Y Cf. A005185, A272610, A272611, A272612, A272613, A278056, A278057, A278058, A278059, A278060, A278061, A278062, A278063, A278064, A278065.

%K nonn

%O 1,2

%A _Nathan Fox_, Nov 13 2016