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A232897
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Number of nonnegative integers not exceeding n which have no decimal digits occurring in n.
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3
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 16, 8, 18, 16, 16, 16, 16, 16, 16, 16, 24, 16, 16, 27, 24, 24, 24, 24, 24, 24, 32, 24, 24, 24, 36, 32, 32, 32, 32, 32, 40, 32, 32, 32, 32, 45, 40, 40, 40, 40, 48, 40, 40, 40, 40, 40, 54, 48, 48, 48, 56
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OFFSET
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0,3
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COMMENTS
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A "digit analog" of Euler function phi(n).
n = 123456789 is the smallest n>1 for which a(n)=1; n = 1023456789 is the smallest n>0 for which a(n) = 0. - Peter J. C. Moses, Dec 02 2013
Indeed, for any k, there exists N = N(k), such that all numbers >=N contain at least k digits. The "part" of them which not contain, say, digit "1",<= (0.9)^k, so the "part" of them which contain no at least one digit <= 10*(0.9)^k. This not exceeds any epsilon>0 for a choice of sufficiently large k=k(epsilon). Thus almost all positive numbers are pandigital (in the sense of A171102). -Vladimir Shevelev, Dec 03 2013
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LINKS
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PROG
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(PARI) a(n)=if(n<9, return(n)); my(d=Set(digits(n))); sum(k=1, n-1, #setintersect(d, Set(digits(k)))==0)+(d[1]>0) \\ Charles R Greathouse IV, Dec 02 2013
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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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