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

1,1

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

Table of n, a(n) for n=1..32.

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

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 *)

Crossrefs

Cf. A071062, A071071, A071072, A071073.

Sequence in context: A248010 A067013 A141607 * A275722 A047820 A248807

Adjacent sequences: A071067 A071068 A071069 * A071071 A071072 A071073

Keyword

fini,full,nice,nonn,base

Author

Benoit Cloitre, May 26 2002

Status

approved