A308479 - OEIS

%I #28 Oct 14 2019 01:26:34

%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,2,3,2,1,1,1,1,1,1,1,1,

%T 1,1,2,1,1,1,1,2,1,1,1,1,4,1,2,1,3,1,1,1,1,1,1,1,1,1,3,4,3,1,1,1,1,2,

%U 1,1,4,1,1,2,3,1,1,1,1,1,8,1,1,2,1,1,3,1,11,1,21,1,1,1,2,5,3,5,0,1,1,2,1,1,3

%N Least k such that k*n and (k+1)*n fail to have a common nonzero digit, or 0 if this property never occurs.

%C a(n) = 0 for the members of A308466.

%H David Radcliffe, <a href="/A308479/b308479.txt">Table of n, a(n) for n = 1..10000</a>

%H David Radcliffe, <a href="https://gist.github.com/Radcliffe/2e0a1810dca175e91dd77c50db1f4b44">Python script for A308479</a>

%F If a(n) = k, then a(10*n) = k.

%e a(3) = 1 since 1*3 and 2*3 have no digit in common;

%e a(12) = 2 since 1*12 and 2*12 have the digit 2 in common, but 2*12 and 3*12 have no nonzero digit in common, thus a(12) = 2;

%e a(25) = 3 since 1*25 and 2*25 have the digit 5 in common, 2*25 and 3*25 have the digit 5 in common, but 3*25 and 4*25 have no nonzero digit in common; etc.

%t a = Compile[{{n, _Integer}}, Module[{k = 1, id1 = DeleteCases[ IntegerDigits[ n], 0], id2 = DeleteCases[ IntegerDigits[ 2n], 0]}, While[k < 1001 && Intersection[id1, id2] != {}, id1 = id2; k++; id2 = DeleteCases[ Union[ IntegerDigits[(k + 1) n]], 0]]; If[k == 1001, 0, k]]]; Array[a, 198]

%Y Cf. A308466.

%K nonn,base

%O 1,12

%A _David Radcliffe_, Daniel Griller, and _Robert G. Wilson v_, May 29 2019