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A296606 Numbers k such that d*k does not contain the digit d for any d in {1,2,3,4,5,6,7,8,9}.

%I A296606 #32 Feb 14 2018 10:57:24
%S A296606 2,4,8,20,24,32,34,38,40,42,52,58,72,74,80,84,92,200,202,204,208,224,
%T A296606 238,240,242,258,284,292,320,334,338,340,342,380,384,400,402,404,408,
%U A296606 420,424,432,472,474,492,520,524,558,572,574,580,584,592,652,692,720
%N A296606 Numbers k such that d*k does not contain the digit d for any d in {1,2,3,4,5,6,7,8,9}.
%C A296606 All terms end in 0, 2, 4, or 8.
%C A296606 A number k ending in 0 is in this sequence if and only if k/10 is in the sequence.
%C A296606 For a number with an odd digit to be in this sequence, the immediately following digit cannot be 0.
%C A296606 For a number with a 6 to be in this sequence, the immediately following digit must be in the 5 to 9 interval.
%C A296606 This sequence has no members with the digit string "67".
%H A296606 Iain Fox, <a href="/A296606/b296606.txt">Table of n, a(n) for n = 1..10000</a>
%e A296606 22*9 = 198, which contains the digit 9 (which is the number by which we multiplied 22) so 22 is not in this sequence.
%t A296606 Select[Range[2, 720, 2], Function[n, AllTrue[Range@ 9, FreeQ[IntegerDigits[n #], #] &]]] (* _Michael De Vlieger_, Dec 16 2017 *)
%o A296606 (PARI) is(k) = for(d=1, 9, if(setsearch(Set(digits(d*k)), d), return(0))); 1 \\ _Iain Fox_, Dec 16 2017
%K A296606 base,nonn
%O A296606 1,1
%A A296606 _J. Lowell_, Dec 16 2017
%E A296606 More terms from _Jon E. Schoenfield_, Dec 16 2017