A213319 Numbers with exactly 12 nonprime substrings (substrings with leading zeros are considered to be nonprime).

10023, 10053, 10067, 10073, 10079, 10093, 10097, 10107, 10112, 10115, 10119, 10122, 10125, 10129, 10141, 10143, 10147, 10152, 10155, 10170, 10174, 10176, 10178, 10181, 10183, 10190, 10194, 10196, 10198, 10212, 10215, 10219

Offset: 1

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• fini
• base

Comments

The sequence is finite. Proof: Each 9-digit number has at least 15 nonprime substrings. Thus, each number with more than 9 digits has >= 15 nonprime substrings, too. Consequently, there is a boundary b<10^9, such that all numbers > b have more than 12 nonprime substrings.

The first term is a(1)=10023=A213302(12). The last term is a(51477)=99733313=A213300(12).

Examples

			a(1)=10023, since 10023 has 12 nonprime substrings (0, 0, 1, 00, 02, 10, 002, 023, 100, 0023, 1002, 10023).
a(51477)=99733313, since there are 11 nonprime substrings (1, 9, 9, 33, 33, 99, 333, 973, 33313, 97333, 733313, 99733313).
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..51477

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.