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

0,2

Comments

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

Links

Table of n, a(n) for n=0..55.

Example

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.

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

Crossrefs

Cf. A002808 (composite numbers).

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

Sequence in context: A301133 A327687 A307623 * A177833 A166162 A228166

Adjacent sequences: A307621 A307622 A307623 * A307625 A307626 A307627

Keyword

nonn,base

Author

Daniel Lignon, Apr 19 2019

Status

approved