A213308 Numbers with exactly one nonprime substring (substrings with leading zeros are considered to be nonprime).

1, 4, 6, 8, 9, 13, 17, 22, 25, 27, 29, 31, 32, 33, 35, 43, 47, 52, 55, 57, 59, 67, 71, 72, 75, 77, 79, 83, 97, 137, 173, 223, 233, 237, 313, 317, 337, 353, 379, 523, 537, 673, 733, 737, 773, 797, 1373, 3137, 3373, 3733, 3797

Offset: 1

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• fini
• base

Comments

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

The first term is a(1)=1=A213302(1). The last term is a(51)=3797=A213300(1).

Examples

			a(1)=1, since 1 has one nonprime substring.
a(51)=3797, since the only nonprime substring of 3797 is 9.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..51

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.