A213311 Numbers with exactly 4 nonprime substrings (substrings with leading zeros are considered to be nonprime).

103, 107, 111, 112, 115, 119, 122, 125, 129, 130, 134, 136, 138, 143, 147, 151, 152, 155, 159, 163, 170, 174, 176, 178, 183, 191, 192, 195, 199, 202, 203, 205, 207, 212, 215, 219, 220, 221, 224, 226, 228, 242, 245, 250

Offset

1,1

Comments

The sequence is finite. Proof: Each 6-digit number has at least 4 nonprime substrings, and each 4-digit number has at least 1 nonprime substring. Thus, each 10-digit number has at least 5 nonprime substrings. Consequently, there is a boundary b, such that all numbers >= b have more than 4 nonprime substrings.

The first term is a(1)=103=A213302(4). The last term is a(653)=373379=A213300(4).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..653

Example

a(1) = 103, since 103 has 4 nonprime substrings (0, 03, 1, 10).
a(653) = 373379, since there are 4 nonprime substrings (9, 33, 3379, 7337).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A074675 A235155 A167841 * A161402 A318295 A165294

Adjacent sequences: A213308 A213309 A213310 * A213312 A213313 A213314

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved