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

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• fini
• base

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).

Examples

			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).
		

Links

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

Crossrefs

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

Cf. A035244, A079307, A213300 - A213321.

Programs

Mathematica

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