OFFSET
0,2
COMMENTS
Equally, this is the total number of distinct numbers that can be obtained by starting with 1 and applying the "Choix de Bruxelles", version 1 (A323286) operation at most n times.
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.
EXAMPLE
After applying Choix de Bruxelles (version 1) twice to 1, we have seen the numbers {1,2,4}, so a(2)=3. After 5 applications, we have seen {1,2,4,8,16,13,26,32,112}, so a(5) = 9.
PROG
(Python)
from itertools import islice
def cdb2(n):
s, out = str(n), {n}
for l in range(1, len(s)+1):
for i in range(len(s)+1-l):
if s[i] == '0': continue
t = int(s[i:i+l])
out.add(int(s[:i] + str(2*t) + s[i+l:]))
if t&1 == 0: out.add(int(s[:i] + str(t//2) + s[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(), 15))) # Michael S. Branicky, Jul 24 2022
CROSSREFS
KEYWORD
nonn,more,base
AUTHOR
N. J. A. Sloane, Jan 15 2019
EXTENSIONS
a(7)-a(16) from Rémy Sigrist, Jan 15 2019
Deleted an incorrect comment. - N. J. A. Sloane, Jan 24 2019
a(17) from Michael S. Branicky, Jul 24 2022
a(18) from Michael S. Branicky, Jul 26 2022
STATUS
approved