OFFSET
1,2
COMMENTS
The differs from the first version (in A323286) in that now n can be reached from n (by using the empty string).
This slight modification of the definition makes the analysis simpler.
The number of numbers that can be reached from n in one step is A323287(n)+1.
The minimal number of steps to reach n starting at 1 is still given by A323454.
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.
Brady Haran and N. J. A. Sloane, The Brussels Choice, Numberphile video (2020)
EXAMPLE
Rows 1 through 20 are:
1, 2,
1, 2, 4,
3, 6,
2, 4, 8,
5, 10,
3, 6, 12,
7, 14,
4, 8, 16,
9, 18,
5, 10, 20,
11, 12, 21, 22,
6, 11, 12, 14, 22, 24,
13, 16, 23, 26,
7, 12, 14, 18, 24, 28,
15, 25, 30, 110,
8, 13, 16, 26, 32, 112,
17, 27, 34, 114,
9, 14, 18, 28, 36, 116,
19, 29, 38, 118,
10, 20, 40
PROG
(Python)
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 sorted(out)
print([c for n in range(1, 21) for c in cdb2(n)]) # Michael S. Branicky, Jul 24 2022
CROSSREFS
KEYWORD
nonn,base,tabf
AUTHOR
N. J. A. Sloane, Jan 22 2019
STATUS
approved