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A034305
Zeroless nonprimes that remain nonprime if any digit is deleted.
12
14, 16, 18, 44, 46, 48, 49, 64, 66, 68, 69, 81, 84, 86, 88, 91, 94, 96, 98, 99, 122, 124, 125, 126, 128, 142, 144, 145, 146, 148, 152, 154, 155, 156, 158, 162, 164, 165, 166, 168, 182, 184, 185, 186, 188, 212, 214, 215, 216, 218, 221, 222, 224, 225, 226, 228
OFFSET
1,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
MATHEMATICA
npQ[n_]:=!PrimeQ[n]&&FreeQ[IntegerDigits[n], 0]&&AllTrue[FromDigits/@ Table[Drop[IntegerDigits[n], {k}], {k, IntegerLength[n]}], !PrimeQ[#]&]; Select[Range[10, 300], npQ](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)
PROG
(Haskell)
a034305 n = a034305_list !! (n-1)
a034305_list = filter f $ drop 9 a052382_list where
f x = a010051' x == 0 &&
(all (== 0) $ map (a010051' . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x))
-- Reinhard Zumkeller, May 10 2015
(PARI) is(n)=my(d=digits(n)); if(#d<2 || vecmin(d)<1 || isprime(n), return(0)); for(i=0, #d-1, if(isprime(fromdigits(vecextract(d, 2^#d-1-2^i))), return(0))); 1 \\ Charles R Greathouse IV, Jun 25 2017
(Python)
from sympy import isprime
def ok(n):
if n < 10 or isprime(n): return False
s = str(n)
return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
print([k for k in range(229) if ok(k)]) # Michael S. Branicky, Jan 15 2023
CROSSREFS
Subsequence of A052382.
Sequence in context: A053425 A178071 A177982 * A091898 A061365 A327822
KEYWORD
base,nonn,nice
EXTENSIONS
Definition corrected by T. D. Noe, Apr 02 2008
Single-digit terms removed again by Georg Fischer, Jun 21 2021
STATUS
approved