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0, 1, 2, 2, 4, 4, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 18, 18, 18, 18, 18, 18, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 72
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internal format)
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OFFSET
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0,3
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COMMENTS
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For n >= 1, a(n) = the smallest term of A051683 >= n.
Can also be obtained by replacing with zeros all other digits except the first (the most significant) in the factorial base representation of n (A007623), then converting back to decimal.
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LINKS
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FORMULA
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Other identities:
For all n >= 0, a(n) = n - A257687(n).
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EXAMPLE
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Factorial base representation (A007623) of 2 is "10", zeroing all except the most significant digit does not change anything, thus a(2) = 2.
Factorial base representation (A007623) of 3 is "11", zeroing all except the most significant digit gives "10", thus a(3) = 2.
Factorial base representation of 23 is "321", zeroing all except the most significant digit gives "300" which is factorial base representation of 18, thus a(23) = 18.
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PROG
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(Python)
from sympy import factorial as f
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a(n):
x=str(a007623(n))
return int(x[0])*f(len(x))
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CROSSREFS
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Cf. also A053644 (analogous sequence for base-2).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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