A100372 Build up the least positive nonprime number from all subsets of decimal digits {0,1,2,3,4,5,6,7,8,9}. The terms are ordered as follows: 1. for fixed k, the k-digit-subsets for design are ordered lexicographically; 2. choose k=1,2,...,9,10-subsets.

1, 22, 33, 4, 55, 6, 77, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 12, 133, 14, 15, 16, 117, 18, 91, 32, 24, 25, 26, 27, 28, 92, 34, 35, 36, 377, 38, 39, 45, 46, 74, 48, 49, 56, 57, 58, 95, 76, 68, 69, 78, 779, 98, 102, 130, 104, 105, 106, 170, 108, 190, 203, 204, 205, 206

Offset

1,2

Comments

Composite analog of A099756. From the 1023 nonempty digit subsets 1022 terms can be designed because 0 is not permitted.

Links

Table of n, a(n) for n=1..66.

Example

For 2-subsets of {1,3},{1,7},{3,7},{7,9} the least composites should have at least two copies of a digit; that is why the solutions {133,117,377,779} have 3 digits.

Mathematica

<<DiscreteMath`Combinatorica` tm=TimeUsed[]; ta={{0}}; upps={100, 1000, 1000, 7000, 70000}; Do[ks1=KSubsets[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, hu]; Table[fla=1; Do[If[Equal[Union[IntegerDigits[n]], Part[ks1, j]]&&Equal[fla, 1]&&!PrimeQ[n], ta=Append[ta, n]; Print[n]; fla=0], {n, 10^(hu-1), Part[upps, hu]}], {j, 1, Length[ks1]}], {hu, 1, 4}]; {ta=Delete[ta, 1], Length[ta], TimeUsed[]-tm}

Crossrefs

Cf. A099756.

Sequence in context: A121019 A167337 A216798 * A084996 A250180 A252078

Adjacent sequences: A100369 A100370 A100371 * A100373 A100374 A100375

Keyword

fini,nonn,base

Author

Labos Elemer, Dec 01 2004

Status

approved