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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}.
3
2, 4, 8, 20, 24, 32, 34, 38, 40, 42, 52, 58, 72, 74, 80, 84, 92, 200, 202, 204, 208, 224, 238, 240, 242, 258, 284, 292, 320, 334, 338, 340, 342, 380, 384, 400, 402, 404, 408, 420, 424, 432, 472, 474, 492, 520, 524, 558, 572, 574, 580, 584, 592, 652, 692, 720
OFFSET
1,1
COMMENTS
All terms end in 0, 2, 4, or 8.
A number k ending in 0 is in this sequence if and only if k/10 is in the sequence.
For a number with an odd digit to be in this sequence, the immediately following digit cannot be 0.
For a number with a 6 to be in this sequence, the immediately following digit must be in the 5 to 9 interval.
This sequence has no members with the digit string "67".
EXAMPLE
22*9 = 198, which contains the digit 9 (which is the number by which we multiplied 22) so 22 is not in this sequence.
MATHEMATICA
Select[Range[2, 720, 2], Function[n, AllTrue[Range@ 9, FreeQ[IntegerDigits[n #], #] &]]] (* Michael De Vlieger, Dec 16 2017 *)
PROG
(PARI) is(k) = for(d=1, 9, if(setsearch(Set(digits(d*k)), d), return(0))); 1 \\ Iain Fox, Dec 16 2017
CROSSREFS
Sequence in context: A014225 A217520 A124154 * A222562 A252891 A102634
KEYWORD
base,nonn
AUTHOR
J. Lowell, Dec 16 2017
EXTENSIONS
More terms from Jon E. Schoenfield, Dec 16 2017
STATUS
approved