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

Author

Daniel Lignon, Apr 19 2019

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A072857 (the same with primes instead of composite numbers) and A307624.

Programs

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