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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. 5

%I

%S 6,20831,20832,20833,9,20834,20835,20836,12,20837,20838,20839,15,

%T 20840,20841,17,20843,18,20843,20845,20846,22,21,41671,41665,9,18,

%U 41680,41683,20839,22,20860,20865,20843,27,36,20867,41670,20834,39

%N 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 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 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 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 Nathan Fox, <a href="/A283887/b283887.txt">Table of n, a(n) for n = 1..68000</a>

%F 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:=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 Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283886, A283888.

%K nonn,fini

%O 1,1

%A _Nathan Fox_, Mar 19 2017

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Last modified February 29 07:39 EST 2020. Contains 332355 sequences. (Running on oeis4.)