A213312 Numbers with exactly 5 nonprime substrings (substrings with leading zeros are considered to be nonprime).

101, 102, 105, 109, 110, 114, 116, 118, 120, 121, 124, 126, 128, 141, 142, 145, 149, 150, 154, 156, 158, 161, 162, 165, 181, 182, 185, 187, 189, 190, 194, 196, 198, 200, 201, 204, 206, 208, 209, 210, 214, 216, 218, 240

Offset

1,1

Comments

The sequence is finite. Proof: Each 7-digit number has at least 6 nonprime substrings. Thus, each number with more than 7 digits has >= 6 nonprime substrings, too. Consequently, there is a boundary b<10^6, such that all numbers > b have more than 5 nonprime substrings.

The first term is a(1)=101=A213302(5). The last term is a(1330)=831373=A213300(5).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..1330

Example

a(1)=101, since 101 has 5 nonprime substrings (0, 01, 1, 1, 10).
a(1330)= 831373, since there are 5 nonprime substrings (1, 8, 831, 8313, 31373).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A134808 A274612 A261448 * A261021 A271642 A164849

Adjacent sequences: A213309 A213310 A213311 * A213313 A213314 A213315

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved