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A323289
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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.
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6
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1, 2, 3, 4, 5, 9, 24, 59, 136, 362, 1365, 5992, 28187, 135951, 689058, 3908456, 24849118, 171022869, 1248075797
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,more,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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