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A342382
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a(0) = 0; for n > 0, a(n) is the least positive integer not occurring earlier such that both the digits in a(n) and the digits in a(n-1)*a(n) are all distinct.
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5
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 18, 17, 20, 21, 23, 26, 24, 27, 25, 29, 28, 30, 31, 34, 37, 35, 36, 38, 39, 32, 40, 41, 43, 42, 45, 48, 52, 49, 50, 47, 51, 46, 53, 56, 54, 57, 60, 58, 62, 59, 68, 64, 61, 65, 63, 72, 69, 67, 70, 71, 73, 74, 76, 78, 80, 79, 82, 75, 81, 83
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OFFSET
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0,3
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COMMENTS
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The sequence is finite, the 18351st term being a(18350) = 41987 beyond which no number exists that has not occurred earlier that has all distinct digits and that 41987*a(n) has all distinct digits. The maximum term is a(18097) = 219087.
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LINKS
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EXAMPLE
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a(1) = 1 as 1 has one distinct digit and a(0)*1 = 0*1 = 0 which has one distinct digit 0.
a(10) = 10 as 10 has two distinct digits and a(9)*10 = 9*10 = 90 which has two distinct digits 9 and 0.
a(11) = 12 as 12 has two distinct digits and a(10)*12 = 10*12 = 120 which has three distinct digits. Note that 11 is the first skipped number as 11 has 1 as a duplicate digit.
a(16) = 19 as 19 has two distinct digits and a(15)*19 = 16*19 = 304 which has three distinct digits. Note that 17 and 18 are skipped as 16*17 = 272 while 16*18 = 288, both of which contain duplicate digits.
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MATHEMATICA
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Block[{a = {0}, k, m = 42000}, Do[k = 1; While[Nand[FreeQ[a, k], AllTrue[DigitCount[a[[-1]]*k], # < 2 &], AllTrue[DigitCount[k], # < 2 &]], If[k > m, Break[]]; k++]; If[k > m, Break[]]; AppendTo[a, k], {i, 76}]; a] (* Michael De Vlieger, Mar 11 2021 *)
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CROSSREFS
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KEYWORD
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nonn,base,fini
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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