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A062115
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Numbers with no prime substring in their decimal expansion.
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6
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0, 1, 4, 6, 8, 9, 10, 14, 16, 18, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 81, 84, 86, 88, 90, 91, 94, 96, 98, 99, 100, 104, 106, 108, 140, 144, 146, 148, 160, 164, 166, 168, 169, 180, 184, 186, 188, 400, 404, 406, 408, 440, 444, 446, 448, 460, 464, 466
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This is a regular language in base 10, a consequence of the finitude of A071062. [Charles R Greathouse IV, Sep 27 2011]
Subsequence of A202259 (right-truncatable nonprimes). Supersequence of A202262 (composite numbers in which all substrings are composite), A202265 (nonprime numbers in which all substrings and reversal substrings are nonprimes). - Jaroslav Krizek, Jan 28 2012
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Jeffrey Shallit, Minimal primes, Journal of Recreational Mathematics 30:2 (1999-2000), pp. 113-117.
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FORMULA
| A039997(a(n)) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 16 2007
Contribution from Charles R Greathouse IV, Mar 23 2010:
(start)
a(n) = O(n^(log_4 10)) = O(n^1.661) because numbers containing only 0,4,6,8 are in this sequence.
a(n) = Omega(n^(log_13637 1000000)) = Omega(n^1.451) for similar reasons; this bound can be increased by considering longer sequences of digits.
(end)
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EXAMPLE
| 25 is not included because 5 is prime.
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PROG
| (Haskell)
a062115 n = a062115_list !! (n-1)
a062115_list = filter ((== 0) . a039997) a084984_list
-- Reinhard Zumkeller, Jan 31 2012
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CROSSREFS
| Subsequence of A084984. [Arkadiusz Wesolowski, Jul 05 2011]
Cf. A071062.
Cf. A163753 (complement).
Sequence in context: A001745 A050695 A035139 * A141613 A072362 A084988
Adjacent sequences: A062112 A062113 A062114 * A062116 A062117 A062118
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KEYWORD
| base,easy,nonn,changed
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AUTHOR
| Erich Friedman (efriedma(AT)stetson.edu), Jun 28 2001
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EXTENSIONS
| Offset corrected by Arkadiusz Wesolowski, Jul 27 2011
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