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A348138
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For any number n with factorial base representation (d_1, ..., d_k), for i = 1..k, let f_i be the number of i's in (d_1, ..., d_k); the factorial base representation of a(n) is (f_1, ..., f_k).
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2
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0, 1, 2, 4, 1, 3, 6, 12, 12, 18, 8, 14, 2, 8, 8, 14, 4, 10, 1, 7, 7, 13, 3, 9, 24, 48, 48, 72, 30, 54, 48, 72, 72, 96, 54, 78, 30, 54, 54, 78, 36, 60, 26, 50, 50, 74, 32, 56, 6, 30, 30, 54, 12, 36, 30, 54, 54, 78, 36, 60, 12, 36, 36, 60, 18, 42, 8, 32, 32, 56
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OFFSET
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0,3
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COMMENTS
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Leading zeros in factorial base representation of n are ignored.
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LINKS
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FORMULA
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a(n) = n iff n = 0 or n is a factorial number (A000142).
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EXAMPLE
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The first terms, in decimal and in factorial base, are:
n a(n) f(n) f(a(n))
-- ---- ---- -------
0 0 0 0
1 1 1 1
2 2 10 10
3 4 11 20
4 1 20 1
5 3 21 11
6 6 100 100
7 12 101 200
8 12 110 200
9 18 111 300
10 8 120 110
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PROG
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(PARI) a(n) = { my (f=[]); for (r=2, oo, if (n==0, return (sum(k=1, #f, f[k]*(#f-k+1)!)), f=concat(f, 0); my (d=n%r); n\=r; if (d, f[d]++))) }
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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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STATUS
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approved
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