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URL: https://oeis.org/A307623

⇱ A307623 - OEIS

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A307623
Numbers that set a record for the number of distinct composite numbers that can be obtained by permuting some subset of their digits.
2
1, 4, 12, 18, 46, 102, 108, 124, 126, 148, 246, 468, 1002, 1008, 1014, 1022, 1023, 1025, 1026, 1068, 1234, 1236, 1245, 1248, 1268, 1458, 2456, 2468, 10023, 10025, 10026, 10068, 10124, 10125, 10146, 10224, 10234, 10236, 10245, 10248, 10458, 12345, 12348, 12369
OFFSET
1,2
LINKS
EXAMPLE
108 is in this sequence because the number of composite numbers which can be obtained by permuting some or all of digits of 108 is larger than the number of composite numbers obtainable in the same way for any smaller integer. With 108, you can form 9 composite numbers: 8, 10, 18, 80, 81, 108, 180, 801, 810. It's impossible to form n >= 9 composite numbers in the same way with any integer < 108.
MATHEMATICA
f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]], 1], CompositeQ]]];
d=-1; res={}; Do[b=f[n]; If[b>d, AppendTo[res, n]; d=b], {n, 10000}]; res
CROSSREFS
Cf. A072857 (the same with primes instead of composite numbers) and A307624.
Sequence in context: A301163 A301133 A327687 * A307624 A177833 A166162
KEYWORD
nonn,base
AUTHOR
Daniel Lignon, Apr 19 2019
STATUS
approved