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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.

%I A100372 #12 Jul 11 2015 10:18:07
%S A100372 1,22,33,4,55,6,77,8,9,10,20,30,40,50,60,70,80,90,12,133,14,15,16,117,
%T A100372 18,91,32,24,25,26,27,28,92,34,35,36,377,38,39,45,46,74,48,49,56,57,
%U A100372 58,95,76,68,69,78,779,98,102,130,104,105,106,170,108,190,203,204,205,206
%N 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.
%C A100372 Composite analog of A099756. From the 1023 nonempty digit subsets 1022 terms can be designed because 0 is not permitted.
%e A100372 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.
%t A100372 <<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}
%Y A100372 Cf. A099756.
%K A100372 fini,nonn,base
%O A100372 1,2
%A A100372 _Labos Elemer_, Dec 01 2004