A213317 Numbers with exactly 10 nonprime substrings (substrings with leading zeros are considered to be nonprime).

1000, 1001, 1004, 1006, 1008, 1040, 1044, 1046, 1048, 1060, 1064, 1066, 1068, 1080, 1081, 1084, 1086, 1088, 1400, 1404, 1406, 1408, 1440, 1444, 1446, 1448, 1460, 1464, 1466, 1468, 1469, 1480, 1484, 1486, 1488, 1600

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 10 nonprime substrings.

The first term is a(1)=1000=A213302(10). The last term is a(20230)=37337397=A213300(10).

Examples

			a(1)=1000, since 1000 has 10 nonprime substrings (0, 0, 0, 1, 00, 00, 10, 000, 100, 1000).
a(20230)= 37337397, since there are 10 nonprime substrings (9, 33, 39, 7337, 7397, 73373, 373373, 733739, 7337397, 37337397).
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..20230

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.