A232897 - OEIS

%I #41 Dec 08 2013 09:56:22

%S 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,

%T 24,16,16,27,24,24,24,24,24,24,32,24,24,24,36,32,32,32,32,32,40,32,32,

%U 32,32,45,40,40,40,40,48,40,40,40,40,40,54,48,48,48,56

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

%C A "digit analog" of Euler function phi(n).

%C 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

%C 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

%C 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

%H Charles R Greathouse IV, <a href="/A232897/b232897.txt">Table of n, a(n) for n = 0..10000</a>

%o (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

%K nonn,base

%O 0,3

%A _Vladimir Shevelev_, Dec 02 2013

%E More terms from _Peter J. C. Moses_, Dec 02 2013