A283885 Relative of Hofstadter Q-sequence: a(n) = max(0, n+3442) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 3443, 3444, 3445, 9, 3446, 3447, 3448, 12, 3449, 3450, 3451, 15, 3452, 3453, 17, 3455, 18, 3455, 3457, 3458, 22, 21, 6895, 6889, 9, 18, 6904, 6907, 3451, 22, 3472, 3477, 3455, 27, 36, 3479, 6894, 3446, 39, 3480, 3486, 3450, 42

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn

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 3442 terms.

Most terms in this sequence appear in long period-5 quasilinear runs. These runs are separated by 11943 other terms, and each run is approximately six times as long as the previous.

The first such run that falls into a predictable pattern begins at index 90682, though there are other similar patterns earlier.

Links

• Nathan Fox, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A005185, A267501, A274058, A278055, A278066, A283884, A283886, A283887, A283888.

Programs

Maple

A283885:=proc(n) option remember: if n <= 0 then max(0, n+3442): else A283885(n-A283885(n-1)) + A283885(n-A283885(n-2)) + A283885(n-A283885(n-3)): fi: end:

Formula

If the index is between 67 and 3443 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+3444, a(7n+2) = 7n+3446, a(7n+3) = 7, a(7n+4) = 2n+6929, a(7n+5) = n+6877, a(7n+6) = 3440.

For nonnegative integers i, if 1 <= 5n + r <= (487329/5)*6^(i+1) - 88639/5, then

a((487329/5)*6^i - 28924/5 + 5n) = 5

a((487329/5)*6^i - 28924/5 + 5n + 1) = (1461987/5)*6^i - 52797/5 + 3n

a((487329/5)*6^i - 28924/5 + 5n + 2) = 3

a((487329/5)*6^i - 28924/5 + 5n + 3) = (487329/5)*6^i - 28909/5 + 5n

a((487329/5)*6^i - 28924/5 + 5n + 4) = (1461987/5)*6^i - 52792/5 + 3n.