A323289 Total number of distinct numbers that can be obtained by starting with 1 and applying the "Choix de Bruxelles", version 2 (A323460) operation at most n times.

1, 2, 3, 4, 5, 9, 24, 59, 136, 362, 1365, 5992, 28187, 135951, 689058, 3908456, 24849118, 171022869, 1248075797

Offset: 0

Author

N. J. A. Sloane, Jan 15 2019

Keywords

• nonn
• more
• base

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.

Examples

			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.
		

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.
• Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, "Choix de Bruxelles": A New Operation on Positive Integers, Local copy.

Crossrefs

Cf. A323286, A323287, A323452 (first differences), A323453, A323460.

Programs

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

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