A307624 - OEIS

%I #23 Aug 11 2019 00:12:24

%S 1,4,12,18,46,103,122,104,102,108,124,128,126,148,246,468,1002,1008,

%T 1137,1077,1014,1055,1044,1022,1124,1126,1079,1145,1037,1224,1266,

%U 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

%N Least number whose digits can be used to form exactly n distinct composite numbers (not necessarily using all digits).

%C a(n) always exists because with 10^n, you can form exactly n composite numbers... but, in general, it's not the least.

%e 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.

%t f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]],  1], CompositeQ]]];

%t t = Table[0, {100}]; Do[ a = f[n]; If[a < 100 && t[[a + 1]] == 0, t[[a + 1]] = n], {n, 100000}]; t

%Y Cf. A002808 (composite numbers).

%Y Cf. A076449 (the same with primes instead of composite numbers) and A307623 (the sequence of corresponding records).

%K nonn,base

%O 0,2

%A _Daniel Lignon_, Apr 19 2019