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.

6, 20831, 20832, 20833, 9, 20834, 20835, 20836, 12, 20837, 20838, 20839, 15, 20840, 20841, 17, 20843, 18, 20843, 20845, 20846, 22, 21, 41671, 41665, 9, 18, 41680, 41683, 20839, 22, 20860, 20865, 20843, 27, 36, 20867, 41670, 20834, 39

Offset

1,1

Comments

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.

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).

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.

Links

Nathan Fox, Table of n, a(n) for n = 1..68000

Formula

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.

Maple

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:

Crossrefs

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283886, A283888.

Sequence in context: A278369 A283886 A278653 * A241650 A368064 A337990

Adjacent sequences: A283884 A283885 A283886 * A283888 A283889 A283890

Keyword

nonn,fini

Author

Nathan Fox, Mar 19 2017

Status

approved