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Numbers with exactly 3 nonprime substrings (substrings with leading zeros are considered to be nonprime).
1

%I #7 Sep 01 2012 11:47:56

%S 10,14,16,18,40,44,46,48,49,60,64,66,68,69,80,81,84,86,88,90,91,94,96,

%T 98,99,117,123,127,132,133,135,139,153,157,167,171,172,175,177,193,

%U 211,213,217,222,225,230,234,236,238,241

%N Numbers with exactly 3 nonprime substrings (substrings with leading zeros are considered to be nonprime).

%C The sequence is finite. Proof: Each 6-digit number has at least 4 nonprime substrings. Thus, each number with more than 6 digits has >= 4 nonprime substrings, too. Consequently, there is a boundary b<10^5, such that all numbers > b have more than 3 nonprime substrings.

%C The first term is a(1)=10=A213302(3). The last term is a(310)=73373=A213300(3).

%H Hieronymus Fischer, <a href="/A213310/b213310.txt">Table of n, a(n) for n = 1..310</a>

%e a(1)=10, since 10 has 3 nonprime substrings (0, 1, 10).

%e a(310)= 73373, since there are 3 nonprime substrings (33, 7337 and 73373).

%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