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

Author

Vladimir Shevelev, Dec 02 2013

Keywords

• nonn
• base

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 do not contain, say, digit "1",<= (0.9)^k, so the "part" of them which do not contain at least one digit <= 10*(0.9)^k. This does not exceed 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

Programs

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

Extensions

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