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A296606
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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}.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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".
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LINKS
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EXAMPLE
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22*9 = 198, which contains the digit 9 (which is the number by which we multiplied 22) so 22 is not in this sequence.
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MATHEMATICA
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Select[Range[2, 720, 2], Function[n, AllTrue[Range@ 9, FreeQ[IntegerDigits[n #], #] &]]] (* Michael De Vlieger, Dec 16 2017 *)
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PROG
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(PARI) is(k) = for(d=1, 9, if(setsearch(Set(digits(d*k)), d), return(0))); 1 \\ Iain Fox, Dec 16 2017
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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