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A307624
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Least number whose digits can be used to form exactly n distinct composite numbers (not necessarily using all digits).
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1
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1, 4, 12, 18, 46, 103, 122, 104, 102, 108, 124, 128, 126, 148, 246, 468, 1002, 1008, 1137, 1077, 1014, 1055, 1044, 1022, 1124, 1126, 1079, 1145, 1037, 1224, 1266, 1448, 1379, 1039, 1367, 1036, 1057, 1034, 1027, 1047, 1024, 1023, 1025, 1029, 1026, 1068, 1247, 1235, 3579, 1234, 1257, 1289, 1239, 1236, 1278, 1245
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OFFSET
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0,2
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COMMENTS
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a(n) always exists because with 10^n, you can form exactly n composite numbers... but, in general, it's not the least.
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LINKS
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EXAMPLE
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The digits of 103 can be used to form the numbers 1, 3, 10, 13, 30, 31, 103, 130, 301, and 310. Of these, exactly 5 are composite (10, 30, 130, 301 = 7*43, and 310). Since 103 is the smallest such number, a(5) = 103.
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MATHEMATICA
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f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]], 1], CompositeQ]]];
t = Table[0, {100}]; Do[ a = f[n]; If[a < 100 && t[[a + 1]] == 0, t[[a + 1]] = n], {n, 100000}]; t
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CROSSREFS
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Cf. A076449 (the same with primes instead of composite numbers) and A307623 (the sequence of corresponding records).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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