A307623 Numbers that set a record for the number of distinct composite numbers that can be obtained by permuting some subset of their digits.

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

Daniel Lignon, Table of n, a(n) for n = 1..74

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

Adjacent sequences: A307620 A307621 A307622 * A307624 A307625 A307626

Keyword

nonn,base

Author

Daniel Lignon, Apr 19 2019

Status

approved