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%I #27 May 29 2019 19:03:55
%S 1,4,12,18,46,102,108,124,126,148,246,468,1002,1008,1014,1022,1023,
%T 1025,1026,1068,1234,1236,1245,1248,1268,1458,2456,2468,10023,10025,
%U 10026,10068,10124,10125,10146,10224,10234,10236,10245,10248,10458,12345,12348,12369
%N Numbers that set a record for the number of distinct composite numbers that can be obtained by permuting some subset of their digits.
%H Daniel Lignon, <a href="/A307623/b307623.txt">Table of n, a(n) for n = 1..74</a>
%e 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.
%t f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]], 1], CompositeQ]]];
%t d=-1; res={};Do[b=f[n];If[b>d,AppendTo[res,n];d=b],{n,10000}];res
%Y Cf. A072857 (the same with primes instead of composite numbers) and A307624.
%K nonn,base
%O 1,2
%A _Daniel Lignon_, Apr 19 2019