A284053 Relative of Hofstadter Q-sequence.

9, 20, 5, 5, 20, 9, 20, 5, 5, 20, 9, 5, 10, 10, 20, 9, 5, 15, 15, 40, 9, 10, 20, 15, 40, 9, 15, 25, 15, 40, 9, 20, 25, 15, 60, 9, 25, 25, 20, 60, 9, 25, 30, 25, 60, 9, 25, 40, 20, 60, 9, 30, 45, 20, 80, 9, 40, 35, 30, 80, 9, 45, 35, 30, 100, 9, 35, 55, 25, 80, 9, 35, 55, 35, 100

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn

Comments

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

Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.

This sequence has a similar structure to A272610. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence also consists of five interleaved sequences: four chaotic sequences and a sequence of all 9's.

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

Links

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

Crossrefs

Cf. A005185, A272610, A283903, A284054.

Programs

Maple

A284053:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 9: elif n = 2 then 20: elif n = 3 then 5: elif n = 4 then 5: elif n = 5 then 20: elif n = 6 then 9: elif n = 7 then 20: elif n = 8 then 5: elif n = 9 then 5: elif n = 10 then 20: elif n = 11 then 9: elif n = 12 then 5: elif n = 13 then 10: elif n = 14 then 10: elif n = 15 then 20: else A284053(n-A284053(n-1)) + A284053(n-A284053(n-2)): fi: end:

Python

from functools import cache
@cache
def a(n):
    if n <= 0: return 0
    if n < 16:
        return [9, 20, 5, 5, 20, 9, 20, 5, 5, 20, 9, 5, 10, 10, 20][n-1]
    return a(n - a(n-1)) + a(n - a(n-2))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Sep 20 2021