A316412 Positive numbers m so that deletion of some or none but not all digits from m yields a noncomposite number.

1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 131, 137, 173, 311, 317

Offset: 1

Author

Matej Kripner, Aug 04 2018

Keywords

• base
• easy
• fini
• full
• nonn

Comments

Subsequence of A068669. It is easy to see that these are the only terms from the said sequence that satisfy our definition; there are no more terms < 10000. If there is one >= 10000 then there would be one in [1000, 9999]. A contradiction hence the sequence is finite and full.

Also noncomposites m (in base 10) for which the concatenation of every subsequence of digits of m is noncomposite (in base 10). - David A. Corneth, Aug 08 2018

Examples

			317 is a member since all its subsequences, i.e., 3, 1, 7, 31, 17, 37, 317, are noncomposite.
313 is not a member since one of its subsequences (33) is composite.
		

Crossrefs

Subsequence of A068669.

Cf. A008578.

Programs

Mathematica

Select[Range[10^3], AllTrue[FromDigits /@ Union@ Rest@ Subsets@ IntegerDigits@ #, ! CompositeQ@ # &] &] (* Michael De Vlieger, Aug 05 2018 *)