A213315 Numbers with exactly 8 nonprime substrings (substrings with leading zeros are considered to be nonprime).

1011, 1012, 1015, 1021, 1022, 1025, 1027, 1029, 1030, 1034, 1036, 1038, 1043, 1047, 1051, 1052, 1055, 1057, 1059, 1061, 1063, 1067, 1070, 1074, 1076, 1078, 1083, 1087, 1091, 1092, 1095, 1101, 1102, 1105, 1110, 1114

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 8 nonprime substrings.

The first term is a(1)=1011=A213302(8). The last term is a(7483)=8313733=A213300(8).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..7483

Example

a(1)=1011, since 1011 has 8 nonprime substrings (0, 1, 1, 1, 01, 10, 011, 1011).
a(7483)= 8313733 since there are 8 nonprime substrings (1, 8, 33, 831, 8313, 13733, 31373, 313733).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A317526 A235775 A262865 * A345906 A035125 A183849

Adjacent sequences: A213312 A213313 A213314 * A213316 A213317 A213318

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved