OFFSET

1,1

COMMENTS

This sequence is defined by a(n) = 0 for n <= 0; a(1) = 7, a(2) = 26, a(3) = 8, a(4) = 8, a(5) = 8, a(6) = 8, a(7) = 8, a(8) = 26, a(9) = 7, a(10) = 8, a(11) = 16, a(12) = 16, a(13) = 16, a(14) = 16, a(15) = 16, a(16) = 26; 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 A272160. That sequence consists of five interleaved sequences: four chaotic sequences and a sequence of all 4's. This sequence appears to consist eventually of eight interleaved sequences: four chaotic sequences, a sequence of all 7's, a sequence of mostly 32's and an few 40's, a sequence of all 24's, and a rapidly growing sequence with successive terms satisfying either the recurrence A(k) = A(k-3) + A(k-4) or the recurrence A(k) = A(k-3) + A(k-5).

If the 26'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

A284054:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 7: elif n = 2 then 26: elif n = 3 then 8: elif n = 4 then 8: elif n = 5 then 8: elif n = 6 then 8: elif n = 7 then 8: elif n = 8 then 26: elif n = 9 then 7: elif n = 10 then 8: elif n = 11 then 16: elif n = 12 then 16: elif n = 13 then 16: elif n = 14 then 16: elif n = 15 then 16: elif n = 16 then 26: else A284054(n-A284054(n-1)) + A284054(n-A284054(n-2)): fi: end:

PROG

(Python)

from functools import lru_cache

@lru_cache(maxsize=None)

def a(n):

if n <= 0: return 0

if n < 17:

return [7, 26, 8, 8, 8, 8, 8, 26, 7, 8, 16, 16, 16, 16, 16, 26][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, Jul 26 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

Nathan Fox, Mar 19 2017

STATUS

approved