A213316 Numbers with exactly 9 nonprime substrings (substrings with leading zeros are considered to be nonprime).

1002, 1003, 1005, 1007, 1009, 1010, 1014, 1016, 1018, 1020, 1024, 1026, 1028, 1041, 1042, 1045, 1049, 1050, 1054, 1056, 1058, 1062, 1065, 1069, 1082, 1085, 1089, 1090, 1094, 1096, 1098, 1099, 1100, 1104, 1106, 1108, 1140, 1144, 1146, 1148

Offset: 1

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• base
• fini

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 9 nonprime substrings.

The first term is a(1) = 1002 = A213302(9). The last term is a(12411) = 9973331 = A213300(9).

Examples

			a(1) = 1002 is in the sequence, since 1002 has 9 nonprime substrings (0,  0, 1, 00, 02, 10, 002, 100, 1002).
a(12411) = 9973331 is in the sequence since there are 9 nonprime substrings (1, 9, 9, 33, 33, 99, 333, 973, 97333).
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..12411

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.