A225619 Composite numbers that remain composite if any digit is deleted (zero and one are not considered prime).

44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 94, 96, 98, 99, 104, 106, 108, 120, 122, 124, 125, 126, 128, 140, 142, 144, 145, 146, 148, 150, 152, 154, 155, 156, 158, 160, 162, 164, 165, 166, 168, 180, 182, 184, 185, 186, 188, 204, 206, 208, 210, 212, 214, 215

Offset: 1

Author

Derek Orr, Aug 04 2013

Keywords

• nonn
• base
• easy

Comments

These are sometimes called "deletable composites".

Examples

			142 is composite. If the 1 is deleted, 42 is composite. If the 4 is deleted, 12 is composite. If the 2 is deleted, 14 is composite. Therefore, 142 is included in this sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Dave Radcliffe, Python program/code

Crossrefs

Cf. A202262 (composite numbers in which all substrings are composite).

Programs

Mathematica

prime01Q[n_] := n == 0 || n == 1 || PrimeQ[n]; okQ[n_] := Module[{d = IntegerDigits[n]}, Not[Or @@ prime01Q /@ Table[FromDigits[Delete[d, i]], {i, Length[d]}]]]; Select[Range[215], ! PrimeQ[#] && okQ[#] &] (* T. D. Noe, Aug 14 2013 *)