A232897 Number of nonnegative integers not exceeding n which have no decimal digits occurring in n.

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

Adjacent sequences: A232894 A232895 A232896 * A232898 A232899 A232900

Keyword

nonn,base

Author

Vladimir Shevelev, Dec 02 2013

Extensions

More terms from Peter J. C. Moses, Dec 02 2013

Status

approved