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A323287
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Number of different numbers that can be obtained from (the decimal expansion of) n by one step of the Choix de Bruxelles, version 1 (A323286) operation.
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4
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1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 5, 3, 5, 3, 5, 3, 5, 3, 2, 4, 6, 4, 6, 4, 6, 4, 6, 4, 2, 3, 5, 3, 5, 3, 5, 3, 5, 3, 2, 4, 6, 4, 6, 4, 6, 4, 6, 4, 2, 3, 5, 3, 5, 3, 5, 3, 5, 3, 2, 4, 6, 4, 6, 4, 6, 4, 6, 4, 2, 3, 5, 3, 5, 3, 5, 3, 5, 3, 2, 4, 6, 4, 6, 4, 6, 4
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OFFSET
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1,2
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COMMENTS
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This is the number of terms in row n of the irregular triangle in A323286.
This is one less than the number of different numbers that can be obtained from (the decimal expansion of) n by one step of the Choix de Bruxelles, version 2 (A323460) operation. In other words, this is one less than the number of terms in row n of the irregular triangle in A323460.
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LINKS
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EXAMPLE
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From 12 we can reach any of 6, 11, 14, 22, 24, so a(12) = 5.
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PROG
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(PARI) a(n, base=10) = { my (d=digits(n, base), s=Set()); for (w=1, #d, for (l=0, #d-w, if (d[l+1], my (h=d[1..l], m=fromdigits(d[l+1..l+w], base), t=d[l+w+1..#d]); s = setunion(s, Set(fromdigits(concat([h, digits(m*2, base), t]), base))); if (m%2==0, s = setunion(s, Set(fromdigits(concat([h, digits(m/2, base), t]), base))))))); #s } \\ Rémy Sigrist, Jan 15 2019
(Python)
def a(n):
s, out = str(n), set()
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 len(out)
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CROSSREFS
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KEYWORD
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nonn,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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