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A213319 Numbers with exactly 12 nonprime substrings (substrings with leading zeros are considered to be nonprime). 1

%I #7 Sep 01 2012 11:49:19

%S 10023,10053,10067,10073,10079,10093,10097,10107,10112,10115,10119,

%T 10122,10125,10129,10141,10143,10147,10152,10155,10170,10174,10176,

%U 10178,10181,10183,10190,10194,10196,10198,10212,10215,10219

%N Numbers with exactly 12 nonprime substrings (substrings with leading zeros are considered to be nonprime).

%C The sequence is finite. Proof: Each 9-digit number has at least 15 nonprime substrings. Thus, each number with more than 9 digits has >= 15 nonprime substrings, too. Consequently, there is a boundary b<10^9, such that all numbers > b have more than 12 nonprime substrings.

%C The first term is a(1)=10023=A213302(12). The last term is a(51477)=99733313=A213300(12).

%H Hieronymus Fischer, <a href="/A213319/b213319.txt">Table of n, a(n) for n = 1..51477</a>

%e a(1)=10023, since 10023 has 12 nonprime substrings (0, 0, 1, 00, 02, 10, 002, 023, 100, 0023, 1002, 10023).

%e a(51477)=99733313, since there are 11 nonprime substrings (1, 9, 9, 33, 33, 99, 333, 973, 33313, 97333, 733313, 99733313).

%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

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