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A213317
Numbers with exactly 10 nonprime substrings (substrings with leading zeros are considered to be nonprime).
1
1000, 1001, 1004, 1006, 1008, 1040, 1044, 1046, 1048, 1060, 1064, 1066, 1068, 1080, 1081, 1084, 1086, 1088, 1400, 1404, 1406, 1408, 1440, 1444, 1446, 1448, 1460, 1464, 1466, 1468, 1469, 1480, 1484, 1486, 1488, 1600
OFFSET
1,1
COMMENTS
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 10 nonprime substrings.
The first term is a(1)=1000=A213302(10). The last term is a(20230)=37337397=A213300(10).
LINKS
EXAMPLE
a(1)=1000, since 1000 has 10 nonprime substrings (0, 0, 0, 1, 00, 00, 10, 000, 100, 1000).
a(20230)= 37337397, since there are 10 nonprime substrings (9, 33, 39, 7337, 7397, 73373, 373373, 733739, 7337397, 37337397).
KEYWORD
nonn,fini,base
AUTHOR
Hieronymus Fischer, Aug 26 2012
STATUS
approved