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

1,1

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 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

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.

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:

Crossrefs

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

Sequence in context: A012205 A156122 A281501 * A280552 A241137 A086065

Adjacent sequences: A283881 A283882 A283883 * A283885 A283886 A283887

Keyword

nonn,look

Author

Nathan Fox, Mar 19 2017

Status

approved