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A323460
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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).
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13
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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