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A213303
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Smallest number with n nonprime substrings (Version 2: substrings with leading zeros are counted as nonprime if the corresponding number is > 0).
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3
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2, 1, 10, 14, 101, 104, 144, 1001, 1014, 1044, 1444, 10010, 10014, 10144, 10444, 14444, 100101, 100104, 100144, 101444, 104444, 144444, 1000144, 1001014, 1001044, 1001444, 1014444, 1044444, 1444444, 10001044, 10001444, 10010144, 10010444, 10014444, 10144444, 10444444, 14444444, 100010144
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OFFSET
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0,1
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COMMENTS
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The sequence is well defined since for each n >= 0 there is a number with n nonprime substrings.
Different from A213304, first different term is a(16).
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LINKS
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FORMULA
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a(m(m+1)/2) = (13*10^(m-1)-4)/9, m>0.
With b(n):=floor((sqrt(8*n-7)-1)/2):
a(n) > 10^b(n), for n>2, a(n) = 10^b(n) for n=1,2.
a(n) >= 10^b(n)+4*10^(n-1-b(n)(b(n)+1)/2)-1)/9, equality holds if n or n+1 is a triangular number > 0 (cf. A000217).
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EXAMPLE
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a(0)=2, since 2 is the least number with zero nonprime substrings.
a(1)=1, since 1 has 1 nonprime substrings.
a(2)=10, since 10 is the least number with 2 nonprime substrings, these are 1 and 10 ('0' will not be counted).
a(3)=14, since 14 is the least number with 3 nonprime substrings, these are 1 and 4 and 14. 10, 11 and 12 only have 2 such substrings.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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