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A188454
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Numbers n whose decimal digits are distinct and no digit divides n.
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1
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23, 27, 29, 34, 37, 38, 43, 46, 47, 49, 53, 54, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 203, 207, 209, 239, 247, 249, 253, 257, 259, 263, 267, 269, 283, 289, 293, 307, 308, 329, 346, 347, 349, 356, 358, 359, 367, 370, 374
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OFFSET
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1,1
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COMMENTS
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These may not contain 1 or have a 2 or 5 as the last digit. They include prime numbers not containing the digit 1 and composites with a smallest prime factor > 10 and obeying the other constraints (e.g. the largest case is 987654203 = 31×31859813.)
The first even case is 34. The first consecutive pair is {37, 38}. {56,57,58,59} is a consecutive quadruple which is the maximal size for such a subset.
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LINKS
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MATHEMATICA
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dddQ[n_]:=Module[{dcn=DigitCount[n]}, Max[dcn]==1&&First[dcn]==0 && Union[ Divisible[n, Select[IntegerDigits[n], #!=0&]]]=={False}]; Select[Range[ 400], dddQ] (* Harvey P. Dale, May 01 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy,base,fini
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AUTHOR
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STATUS
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approved
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