A283884 Relative of Hofstadter Q-sequence: a(n) = max(0, n+193) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 194, 195, 196, 9, 197, 198, 199, 12, 200, 201, 202, 15, 203, 204, 17, 206, 18, 206, 208, 209, 22, 21, 397, 391, 9, 18, 406, 409, 202, 22, 223, 228, 206, 27, 36, 230, 396, 197, 39, 231, 237, 201, 42, 233, 240, 16, 232, 240, 220, 40

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn
• look

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 193 terms.

Most terms in this sequence appear in long period-5 quasilinear runs. These runs are separated by 441 other terms, and each run is approximately six times as long as the previous.

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005185, A267501, A274058, A278055, A278066, A283885, A283886, A283887, A283888.

Programs

Maple

A283884:=proc(n) option remember: if n <= 0 then max(0, n+193): else A283884(n-A283884(n-1)) + A283884(n-A283884(n-2)) + A283884(n-A283884(n-3)): fi: end:

Formula

If the index is between 67 and 195 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+195, a(7n+2) = 7n+197, a(7n+3) = 7, a(7n+4) = 2n+431, a(7n+5) = n+379, a(7n+6) = 191.

For nonnegative integers i, if 1<=5n+r<=(2417/5)*6^(i+1)-3382/5, then

a((2417/5)*6^i-1177/5+5n) = 5

a((2417/5)*6^i-1177/5+5n+1) = (7251/5)*6^i - 2046/5 + 3n

a((2417/5)*6^i-1177/5+5n+2) = 3

a((2417/5)*6^i-1177/5+5n+3) = (2417/5)*6^i - 1162/5 + 5n

a((2417/5)*6^i-1177/5+5n+4) = (7251/5)*6^i - 2041/5 + 3n.