cp's OEIS Frontend

A283885 Relative of Hofstadter Q-sequence: a(n) = max(0, n+3442) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

%I A283885 #6 Mar 19 2017 19:24:40
%S A283885 6,3443,3444,3445,9,3446,3447,3448,12,3449,3450,3451,15,3452,3453,17,
%T A283885 3455,18,3455,3457,3458,22,21,6895,6889,9,18,6904,6907,3451,22,3472,
%U A283885 3477,3455,27,36,3479,6894,3446,39,3480,3486,3450,42
%N A283885 Relative of Hofstadter Q-sequence: a(n) = max(0, n+3442) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.
%C A283885 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 3442 terms.
%C A283885 Most terms in this sequence appear in long period-5 quasilinear runs. These runs are separated by 11943 other terms, and each run is approximately six times as long as the previous.
%C A283885 The first such run that falls into a predictable pattern begins at index 90682, though there are other similar patterns earlier.
%H A283885 Nathan Fox, <a href="/A283885/b283885.txt">Table of n, a(n) for n = 1..100000</a>
%F A283885 If the index is between 67 and 3443 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+3444, a(7n+2) = 7n+3446, a(7n+3) = 7, a(7n+4) = 2n+6929, a(7n+5) = n+6877, a(7n+6) = 3440.
%F A283885 For nonnegative integers i, if 1 <= 5n + r <= (487329/5)*6^(i+1) - 88639/5, then
%F A283885 a((487329/5)*6^i - 28924/5 + 5n) = 5
%F A283885 a((487329/5)*6^i - 28924/5 + 5n + 1) = (1461987/5)*6^i - 52797/5 + 3n
%F A283885 a((487329/5)*6^i - 28924/5 + 5n + 2) = 3
%F A283885 a((487329/5)*6^i - 28924/5 + 5n + 3) = (487329/5)*6^i - 28909/5 + 5n
%F A283885 a((487329/5)*6^i - 28924/5 + 5n + 4) = (1461987/5)*6^i - 52792/5 + 3n.
%p A283885 A283885:=proc(n) option remember: if n <= 0 then max(0, n+3442): else A283885(n-A283885(n-1)) + A283885(n-A283885(n-2)) + A283885(n-A283885(n-3)): fi: end:
%Y A283885 Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283886, A283887, A283888.
%K A283885 nonn
%O A283885 1,1
%A A283885 _Nathan Fox_, Mar 19 2017