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A034305 Zeroless nonprimes that remain nonprime if any digit is deleted.

%I A034305 #39 Jan 15 2023 19:50:12
%S A034305 14,16,18,44,46,48,49,64,66,68,69,81,84,86,88,91,94,96,98,99,122,124,
%T A034305 125,126,128,142,144,145,146,148,152,154,155,156,158,162,164,165,166,
%U A034305 168,182,184,185,186,188,212,214,215,216,218,221,222,224,225,226,228
%N A034305 Zeroless nonprimes that remain nonprime if any digit is deleted.
%H A034305 Reinhard Zumkeller, <a href="/A034305/b034305.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%t A034305 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 *)
%o A034305 (Haskell)
%o A034305 a034305 n = a034305_list !! (n-1)
%o A034305 a034305_list = filter f $ drop 9 a052382_list where
%o A034305   f x = a010051' x == 0 &&
%o A034305         (all (== 0) $ map (a010051' . read) $
%o A034305          zipWith (++) (inits $ show x) (tail $ tails $ show x))
%o A034305 -- _Reinhard Zumkeller_, May 10 2015
%o A034305 (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
%o A034305 (Python)
%o A034305 from sympy import isprime
%o A034305 def ok(n):
%o A034305     if n < 10 or isprime(n): return False
%o A034305     s = str(n)
%o A034305     return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
%o A034305 print([k for k in range(229) if ok(k)]) # _Michael S. Branicky_, Jan 15 2023
%Y A034305 Subsequence of A052382.
%Y A034305 Cf. A034302, A034303, A034304, A010051.
%K A034305 base,nonn,nice
%O A034305 1,1
%A A034305 _David W. Wilson_
%E A034305 Definition corrected by _T. D. Noe_, Apr 02 2008
%E A034305 Single-digit terms removed again by _Georg Fischer_, Jun 21 2021