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

1,1

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).

Links

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

Example

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).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A033432 A169732 A169734 * A281150 A069746 A291346

Adjacent sequences: A213314 A213315 A213316 * A213318 A213319 A213320

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved