A213313 - OEIS

%I #12 Apr 08 2019 08:42:06

%S 100,104,106,108,140,144,146,148,160,164,166,168,169,180,184,186,188,

%T 400,404,406,408,440,444,446,448,460,464,466,468,469,480,481,484,486,

%U 488,490,494,496,498,600,604,606,608,609

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

%C 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.

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

%H Hieronymus Fischer, <a href="/A213313/b213313.txt">Table of n, a(n) for n = 1..2351</a>

%e a(1)=100, since 100 has 6 nonprime substrings (0, 0, 00, 1, 10, 100).

%e a(2351)= 3733797, since there are 6 nonprime substrings (9, 33, 3379, 7337, 733797, 3733797).

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

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

%Y Cf. A035244, A079307, A213300 - A213321.

%K nonn,fini,base

%O 1,1

%A _Hieronymus Fischer_, Aug 26 2012