A284053 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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:

PROG

(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

CROSSREFS

Cf. A005185, A272610, A283903, A284054.