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.
FORMULA
A039997(a(n)) = 0. - Reinhard Zumkeller, Jul 16 2007
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
(Python)
from sympy import isprime
def ok(n):
s = str(n)
ss = (int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))
return not any(isprime(k) for k in ss)
print([k for k in range(500) if ok(k)]) # Michael S. Branicky, May 02 2023
(Python) # faster for initial segment of sequence; uses ok, import above
from itertools import chain, count, islice, product
def agen(): # generator of terms
yield from chain((0, ), (int(t) for t in (f+"".join(r) for d in count(1) for f in "14689" for r in product("014689", repeat=d-1)) if ok(t)))
print(list(islice(agen(), 100))) # Michael S. Branicky, May 02 2023
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jun 28 2001
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Jul 27 2011
STATUS
approved