A213313 Numbers with exactly 6 nonprime substrings (substrings with leading zeros are considered to be nonprime).

100, 104, 106, 108, 140, 144, 146, 148, 160, 164, 166, 168, 169, 180, 184, 186, 188, 400, 404, 406, 408, 440, 444, 446, 448, 460, 464, 466, 468, 469, 480, 481, 484, 486, 488, 490, 494, 496, 498, 600, 604, 606, 608, 609

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 6 nonprime substrings.

The first term is a(1)=100=A213302(6). The last term is a(2351)=3733797=A213300(6).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..2351

Example

a(1)=100, since 100 has 6 nonprime substrings (0, 0, 00, 1, 10, 100).
a(2351)= 3733797, since there are 6 nonprime substrings (9, 33, 3379, 7337, 733797, 3733797).

Mathematica

Select[Range[700], Count[FromDigits/@Flatten[Table[Partition[ IntegerDigits[ #], n, 1], {n, IntegerLength[#]}], 1], _?(!PrimeQ[#]&)]==6&] (* Harvey P. Dale, Apr 08 2019 *)

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Sequence in context: A204582 A204583 A092633 * A204584 A108343 A349771

Adjacent sequences: A213310 A213311 A213312 * A213314 A213315 A213316

Keyword

nonn,fini,base

Author

Hieronymus Fischer, Aug 26 2012

Status

approved