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

Author

Daniel Lignon, Oct 19 2018

Keywords

• nonn
• base
• fini
• full

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.

Examples

			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.
		

Crossrefs

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

Programs

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 *)