A356511 Total number of distinct numbers that can be obtained by starting with 1 and applying the "Choix de Bruxelles", version 2 operation at most n times in duodecimal (base 12).

1, 2, 3, 4, 5, 9, 19, 45, 107, 275, 778, 2581, 10170, 45237, 222859, 1191214, 6887258, 42894933, 287397837

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.

J. Conrad, Python program.

Example

For n=4, the a(4) = 5 numbers obtained are (in base 12): 1, 2, 4, 8, 14.
For n=5, they expand to a(5) = 9 numbers (in base 12): 1, 2, 4, 8, 12, 14, 18, 24, 28.

Prog

(Python) See links
(Python)
from itertools import islice
from sympy.ntheory import digits
def fd12(d): return sum(12**i*di for i, di in enumerate(d[::-1]))
def cdb2(n):
    d, out = digits(n, 12)[1:], {n}
    for l in range(1, len(d)+1):
        for i in range(len(d)+1-l):
            if d[i] == 0: continue
            t = fd12(d[i:i+l])
            out.add(fd12(d[:i] + digits(2*t, 12)[1:] + d[i+l:]))
            if t&1 == 0:
                out.add(fd12(d[:i] + digits(t//2, 12)[1:] + d[i+l:]))
    return out
def agen():
    reach, expand = {1}, [1]
    while True:
        yield len(reach)
        newreach = {r for q in expand for r in cdb2(q) if r not in reach}
        reach |= newreach
        expand = list(newreach)
print(list(islice(agen(), 14))) # Michael S. Branicky, Aug 17 2022

Crossrefs

Cf. A323289 (decimal).

Sequence in context: A305237 A088817 A018896 * A162374 A323289 A355374

Adjacent sequences: A356508 A356509 A356510 * A356512 A356513 A356514

Keyword

nonn,more,base

Author

J. Conrad, Aug 09 2022

Extensions

a(16)-a(18) from Michael S. Branicky, Aug 17 2022

Status

approved