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A323460 Choix de Bruxelles, version 2: irregular table read by rows in which row n lists all the legal numbers that can be reached by halving or doubling some substring of the decimal expansion of n (including the empty string). 13
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 (list; graph; refs; listen; history; text; internal format)
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 Neil 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
Sequence in context: A364780 A124904 A187500 * A129144 A360594 A295313
KEYWORD
nonn,base,tabf
AUTHOR
N. J. A. Sloane, Jan 22 2019
STATUS
approved

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)