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A213316
Numbers with exactly 9 nonprime substrings (substrings with leading zeros are considered to be nonprime).
1
1002, 1003, 1005, 1007, 1009, 1010, 1014, 1016, 1018, 1020, 1024, 1026, 1028, 1041, 1042, 1045, 1049, 1050, 1054, 1056, 1058, 1062, 1065, 1069, 1082, 1085, 1089, 1090, 1094, 1096, 1098, 1099, 1100, 1104, 1106, 1108, 1140, 1144, 1146, 1148
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 9 nonprime substrings.
The first term is a(1) = 1002 = A213302(9). The last term is a(12411) = 9973331 = A213300(9).
LINKS
EXAMPLE
a(1) = 1002 is in the sequence, since 1002 has 9 nonprime substrings (0, 0, 1, 00, 02, 10, 002, 100, 1002).
a(12411) = 9973331 is in the sequence since there are 9 nonprime substrings (1, 9, 9, 33, 33, 99, 333, 973, 97333).
KEYWORD
nonn,base,fini
AUTHOR
Hieronymus Fischer, Aug 26 2012
STATUS
approved