A213310 Numbers with exactly 3 nonprime substrings (substrings with leading zeros are considered to be nonprime).

10, 14, 16, 18, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 81, 84, 86, 88, 90, 91, 94, 96, 98, 99, 117, 123, 127, 132, 133, 135, 139, 153, 157, 167, 171, 172, 175, 177, 193, 211, 213, 217, 222, 225, 230, 234, 236, 238, 241

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 3 nonprime substrings.

The first term is a(1)=10=A213302(3). The last term is a(310)=73373=A213300(3).

Examples

			a(1)=10, since 10 has 3 nonprime substrings (0, 1, 10).
a(310)= 73373, since there are 3 nonprime substrings (33, 7337 and 73373).
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..310

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.