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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 10-automatic sequence, 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

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.

Index entries for 10-automatic 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 !! (n-1)

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

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Last modified August 14 01:55 EDT 2020. Contains 336476 sequences. (Running on oeis4.)