A283903 Relative of Hofstadter Q-sequence.

11, 20, 6, 6, 6, 20, 11, 20, 6, 6, 6, 20, 11, 6, 12, 12, 12, 20, 11, 6, 18, 18, 12, 40, 11, 12, 24, 18, 12, 40, 11, 18, 30, 18, 18, 40, 11, 24, 30, 18, 18, 80, 11, 30, 30, 24, 24, 80, 11, 30, 36, 30, 24, 80, 11, 30, 48, 24, 24, 80, 11, 36, 54, 24, 24, 160, 11, 48, 42, 36, 30, 120, 11, 54, 42

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn
• fini
• full

Comments

This sequence is defined by a(n) = 0 for n <= 0; a(1) = 11, a(2) = 20, a(3) = 6, a(4) = 6, a(5) = 6, a(6) = 20, a(7) = 11, a(8) = 20, a(9) = 6, a(10) = 6, a(11) = 6, a(12) = 20, a(13) = 11, a(14) = 6, a(15) = 12, a(16) = 12, a(17) = 12, a(18) = 20; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

Similar to Hofstadter's Q-sequence A005185 but with different starting values.

For as long as it exists, this sequence has a similar structure to A272160. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence consists of six interleaved sequences: five chaotic sequences and a sequence of all 11's.

If the 20's in the initial condition are each replaced by larger numbers, the general structure of this sequence does not change.

This sequence has exactly 2179 terms, since a(2179)=0 and computing a(2180) would refer to itself.

Links

• Nathan Fox, Table of n, a(n) for n = 1..2179

Crossrefs

Cf. A005185, A272610, A284053, A284054.

Programs

Maple

A283903:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 11: elif n = 2 then 20: elif n = 3 then 6: elif n = 4 then 6: elif n = 5 then 6: elif n = 6 then 20: elif n = 7 then 11: elif n = 8 then 20: elif n = 9 then 6: elif n = 10 then 6: elif n = 11 then 6: elif n = 12 then 20: elif n = 13 then 11: elif n = 14 then 6: elif n = 15 then 12: elif n = 16 then 12: elif n = 17 then 12: elif n = 18 then 20: else A283903(n-A283903(n-1)) + A283903(n-A283903(n-2)): fi: end: