A283886 Relative of Hofstadter Q-sequence: a(n) = max(0, n+19395) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 19396, 19397, 19398, 9, 19399, 19400, 19401, 12, 19402, 19403, 19404, 15, 19405, 19406, 17, 19408, 18, 19408, 19410, 19411, 22, 21, 38801, 38795, 9, 18, 38810, 38813, 19404, 22, 19425, 19430, 19408, 27, 36, 19432, 38800, 19399, 39

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn
• fini

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 19395 terms.

Most terms in this sequence appear in a long pattern stretching from a(58340) through a(80425266), of 16 interleaved sequences.

This sequence has exactly 80425397 terms (of positive index). a(80425397) = 0, so an attempt to calculate a(80425398) would refer to itself.

Links

• Nathan Fox, Table of n, a(n) for n = 1..61000

Crossrefs

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283885, A283887, A283888.

Programs

Maple

A283886:=proc(n) option remember: if n <= 0 then max(0, n+19395): else A283886(n-A283886(n-1)) + A283886(n-A283886(n-2)) + A283886(n-A283886(n-3)): fi: end:

Formula

If the index is between 67 and 19396 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+19397, a(7n+2) = 7n+19399, a(7n+3) = 7, a(7n+4) = 2n+38835, a(7n+5) = n+38783, a(7n+6) = 19393.