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

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• fini
• base

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).

Examples

			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).
		

Links

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

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.