A213314 Numbers with exactly 7 nonprime substrings (substrings with leading zeros are considered to be nonprime).

1017, 1019, 1023, 1032, 1035, 1039, 1053, 1071, 1072, 1075, 1077, 1079, 1093, 1107, 1109, 1111, 1112, 1115, 1119, 1122, 1125, 1143, 1147, 1152, 1155, 1159, 1170, 1174, 1176, 1178, 1181, 1183, 1187, 1191, 1192, 1195

Offset

1,1

Comments

The sequence is finite. Proof: Each 8-digit number has at least 10 nonprime substrings. Thus, each number with more than 8 digits has >= 10 nonprime substrings, too. Consequently, there is a boundary b<10^7, such that all numbers > b have more than 7 nonprime substrings.

The first term is a(1)=1017=A213302(7). The last term is a(4362)=3733739=A213300(7).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..4362

Example

a(1)=1017, since 1017 has 7 nonprime substrings (0, 1, 1, 01, 10, 017, 1017).
a(4362)= 3733739 since there are 7 nonprime substrings (9, 33, 39, 7337, 73373, 373373, 733739).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A023083 A221808 A202905 * A054035 A087837 A235811

Adjacent sequences: A213311 A213312 A213313 * A213315 A213316 A213317

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved