A034305 - OEIS

%I #39 Jan 15 2023 19:50:12

%S 14,16,18,44,46,48,49,64,66,68,69,81,84,86,88,91,94,96,98,99,122,124,

%T 125,126,128,142,144,145,146,148,152,154,155,156,158,162,164,165,166,

%U 168,182,184,185,186,188,212,214,215,216,218,221,222,224,225,226,228

%N Zeroless nonprimes that remain nonprime if any digit is deleted.

%H 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 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 (Haskell)

%o a034305 n = a034305_list !! (n-1)

%o a034305_list = filter f $ drop 9 a052382_list where

%o   f x = a010051' x == 0 &&

%o         (all (== 0) $ map (a010051' . read) $

%o          zipWith (++) (inits $ show x) (tail $ tails $ show x))

%o -- _Reinhard Zumkeller_, May 10 2015

%o (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 (Python)

%o from sympy import isprime

%o def ok(n):

%o     if n < 10 or isprime(n): return False

%o     s = str(n)

%o     return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))

%o print([k for k in range(229) if ok(k)]) # _Michael S. Branicky_, Jan 15 2023

%Y Subsequence of A052382.

%Y Cf. A034302, A034303, A034304, A010051.

%K base,nonn,nice

%O 1,1

%A _David W. Wilson_

%E Definition corrected by _T. D. Noe_, Apr 02 2008

%E Single-digit terms removed again by _Georg Fischer_, Jun 21 2021