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A232897
Number of nonnegative integers not exceeding n which have no decimal digits occurring in n.
3
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
OFFSET
0,3
COMMENTS
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
If n > 0, a(n) = 0 if and only if n is in A171102; consequently a(n) = 0 for almost all n. - Charles R Greathouse IV, 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
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
PROG
(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
CROSSREFS
Sequence in context: A017894 A291571 A341191 * A309166 A028903 A081599
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Dec 02 2013
EXTENSIONS
More terms from Peter J. C. Moses, Dec 02 2013
STATUS
approved