A307624 Least number whose digits can be used to form exactly n distinct composite numbers (not necessarily using all digits).

1, 4, 12, 18, 46, 103, 122, 104, 102, 108, 124, 128, 126, 148, 246, 468, 1002, 1008, 1137, 1077, 1014, 1055, 1044, 1022, 1124, 1126, 1079, 1145, 1037, 1224, 1266, 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

Offset: 0

Author

Daniel Lignon, Apr 19 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Crossrefs

Cf. A002808 (composite numbers).

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

Programs

Mathematica

f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]],  1], CompositeQ]]];
t = Table[0, {100}]; Do[ a = f[n]; If[a < 100 && t[[a + 1]] == 0, t[[a + 1]] = n], {n, 100000}]; t