A213309 Numbers with exactly 2 nonprime substrings (substrings with leading zeros are considered to be nonprime).

11, 12, 15, 19, 20, 21, 24, 26, 28, 30, 34, 36, 38, 39, 41, 42, 45, 50, 51, 54, 56, 58, 61, 62, 63, 65, 70, 74, 76, 78, 82, 85, 87, 89, 92, 93, 95, 113, 131, 179, 197, 227, 229, 231, 232, 235, 239, 253, 257, 271, 273, 277, 283

Offset: 1

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• fini
• base

Comments

The sequence is finite. Proof: Each 6-digit number has at least 4 nonprime substrings. Thus, each number with more than 6 digits has >= 4 nonprime substrings, too. Consequently, there is a boundary b<10^5, such that all numbers > b have more than 2 nonprime substrings.

The first term is a(1)=11=A213302(2). The last term is a(130)=37337=A213300(2).

Examples

			a(1)=11, since 11 has 2 nonprime substrings.
a(130)= 37337, since there are 2 nonprime substrings (33 and 337).
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..130

Crossrefs

Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685.

Cf. A035244, A079307, A213300 - A213321.