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A298372
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a(n), in decimal base, is the number of numbers k >= 0 with no more digits than n such that k + n can be computed without carry.
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2
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1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 90, 81, 72, 63, 54, 45, 36, 27, 18, 9, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8, 70, 63, 56, 49, 42, 35, 28, 21, 14, 7, 60, 54, 48, 42, 36, 30, 24, 18, 12, 6, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 40, 36, 32, 28, 24, 20, 16, 12, 8
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OFFSET
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0,2
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COMMENTS
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We consider here that 0 has no digit, and hence a(0) = 1.
The corresponding sequence for the binary base is A080100.
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LINKS
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FORMULA
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a(0) = 1.
a(10 * k + d) = a(k) * (10 - d) when 10 * k + d > 0 and 0 <= d < 10.
a(n) = Product_{ d = 0..9 } (10 - d)^A100910(n, d) for any n > 0.
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EXAMPLE
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a(42) = (10 - 4) * (10 - 2) = 48.
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PROG
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(PARI) a(n, {base=10}) = my (d=digits(n, base)); prod(i=1, #d, base-d[i])
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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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