

A062115


Numbers with no prime substring in their decimal expansion.


9



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;
text;
internal format)



OFFSET

1,3


COMMENTS

This is a 10automatic sequence, a consequence of the finitude of A071062.  Charles R Greathouse IV, Sep 27 2011
Subsequence of A202259 (righttruncatable 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


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Jeffrey Shallit, Minimal primes, Journal of Recreational Mathematics 30:2 (19992000), pp. 113117.
Index entries for 10automatic sequences.


FORMULA

A039997(a(n)) = 0.  Reinhard Zumkeller, 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)


EXAMPLE

25 is not included because 5 is prime.


PROG

(Haskell)
a062115 n = a062115_list !! (n1)
a062115_list = filter ((== 0) . a039997) a084984_list
 Reinhard Zumkeller, Jan 31 2012


CROSSREFS

Subsequence of A084984. [Arkadiusz Wesolowski, Jul 05 2011]
Cf. A071062.
Cf. A163753 (complement).
Sequence in context: A050695 A035139 A316227 * A141613 A072362 A278948
Adjacent sequences: A062112 A062113 A062114 * A062116 A062117 A062118


KEYWORD

base,easy,nonn


AUTHOR

Erich Friedman, Jun 28 2001


EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Jul 27 2011


STATUS

approved



