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

1,2

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).

Links

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

Example

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

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A020201 A292079 A161760 * A067127 A119492 A285586

Adjacent sequences: A213305 A213306 A213307 * A213309 A213310 A213311

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved