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

1,1

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).

Links

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

Example

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).

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A204575 A139105 A262596 * A169828 A151956 A111349

Adjacent sequences: A213313 A213314 A213315 * A213317 A213318 A213319

Keyword

nonn,base,fini

Author

Hieronymus Fischer, Aug 26 2012

Status

approved