A320726 Composite numbers such that all other numbers obtained from all permutations of all subsets of the digits are noncomposite.

4, 6, 8, 9, 10, 20, 22, 30, 32, 33, 35, 50, 55, 70, 77, 111

Offset

1,1

Comments

Sequence is finite since it is a subsequence of a finite sequence (A071070).

This is complete: there are only 16 terms in the sequence.

Links

Table of n, a(n) for n=1..16.

Example

371 is in this sequence because it's composite and none of the numbers 1, 3, 7, 13, 17, 31, 37, 137, 173, 317, 713 and 731 is composite.

Mathematica

Select[Range[4, 10^3], Function[n, And[CompositeQ@ n, NoneTrue[DeleteCases[Flatten@ Map[If[Length@ # > 1, FromDigits /@ Permutations@ #, #] &, Rest@ Subsets@ IntegerDigits@ n], _?(# == n &)], CompositeQ]]]] (* Michael De Vlieger, Nov 13 2018 *)

Crossrefs

Subsequence of A071070. Cf. A320725 (the same for prime numbers).

Sequence in context: A202265 A004716 A212372 * A205530 A100373 A211302

Adjacent sequences: A320723 A320724 A320725 * A320727 A320728 A320729

Keyword

nonn,base,fini,full

Author

Daniel Lignon, Oct 19 2018

Status

approved