A071070 Minimal set of composite-strings in base 10.

4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, 711, 713, 731

Offset: 1

Author

Benoit Cloitre, May 26 2002

Keywords

• fini
• full
• nice
• nonn
• base

Comments

Any composite number contains in its digits at least one of the term of this sequence and there is no smaller set.

References

• J.-P. Delahaye, "Pour la science", (French edition of Scientific American), Juin 2002, p. 99
• J. Shallit, Minimal primes, in J.Recreational Mathematics, vol. 30.2, pp. 113-117,1999-2000

Links

• J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.

Crossrefs

Cf. A071062, A071071, A071072, A071073.

Programs

Mathematica

subs[digits_List] := Select[Subsets[digits], CompositeQ[FromDigits[#]]&] //. {a___List, b_List, c___List, d_List, e___List} /; MemberQ[Subsets[d], b] :> {a, b, c, e};
aa = {};
Do[aa = Union[aa, subs[IntegerDigits[n]]], {n, Select[Range[1000], CompositeQ]}];
A071070 = FromDigits /@ aa (* Jean-François Alcover, Dec 20 2017 *)