OFFSET
0,2
LINKS
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
KEYWORD
nonn,more,base
AUTHOR
J. Conrad, Aug 09 2022
EXTENSIONS
a(16)-a(18) from Michael S. Branicky, Aug 17 2022
STATUS
approved