cp's OEIS Frontend

A283887 Relative of Hofstadter Q-sequence: a(n) = max(0, n+20830) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

%I A283887 #6 Mar 19 2017 19:24:52
%S A283887 6,20831,20832,20833,9,20834,20835,20836,12,20837,20838,20839,15,
%T A283887 20840,20841,17,20843,18,20843,20845,20846,22,21,41671,41665,9,18,
%U A283887 41680,41683,20839,22,20860,20865,20843,27,36,20867,41670,20834,39
%N A283887 Relative of Hofstadter Q-sequence: a(n) = max(0, n+20830) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.
%C A283887 Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 20830 terms.
%C A283887 Most terms in this sequence appear in one of two long patterns of 16 interleaved sequences. The first stretches from a(64180) through a(9029945). The second stretches from a(9029971) through a(-20830 + 84975*2^560362).
%C A283887 This sequence has exactly -20799 + 84975*2^560362 terms (of positive index). a(-20799 + 84975*2^560362) = 0, so an attempt to calculate a(-20798 + 84975*2^560362) would refer to itself.
%H A283887 Nathan Fox, <a href="/A283887/b283887.txt">Table of n, a(n) for n = 1..68000</a>
%F A283887 If the index is between 67 and 20831 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+20832, a(7n+2) = 7n+20834, a(7n+3) = 7, a(7n+4) = 2n+41705, a(7n+5) = n+41653, a(7n+6) = 20828.
%p A283887 A283887:=proc(n) option remember: if n <= 0 then max(0, n+20830): else A283887(n-A283887(n-1)) + A283887(n-A283887(n-2)) + A283887(n-A283887(n-3)): fi: end:
%Y A283887 Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283886, A283888.
%K A283887 nonn,fini
%O A283887 1,1
%A A283887 _Nathan Fox_, Mar 19 2017