A283903 -id:A283903 - cp's OEIS frontend

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

Nathan Fox, Mar 19 2017

nonn

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.

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

Cf. A005185, A272610, A283903, A284054.

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:

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

A284054 Relative of Hofstadter Q-sequence.

Original entry on oeis.org

7, 26, 8, 8, 8, 8, 8, 26, 7, 8, 16, 16, 16, 16, 16, 26, 7, 16, 24, 8, 16, 24, 8, 26, 7, 24, 16, 24, 24, 16, 24, 52, 7, 16, 48, 8, 24, 32, 24, 52, 7, 48, 8, 8, 48, 32, 16, 78, 7, 8, 16, 16, 48, 40, 24, 78, 7, 16, 24, 16, 72, 32, 24, 104, 7, 24, 24, 16, 96, 40, 24, 130, 7, 24, 32

Offset: 1

Nathan Fox, Mar 19 2017

nonn

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.

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

Cf. A005185, A272610, A283903, A284053.

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:

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

cp's OEIS Frontend

A284053 Relative of Hofstadter Q-sequence.

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