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A034302 Zeroless primes that remain prime if any digit is deleted.

%I A034302 #43 Jan 15 2024 19:04:02
%S A034302 23,37,53,73,113,131,137,173,179,197,311,317,431,617,719,1499,1997,
%T A034302 2239,2293,3137,4919,6173,7433,9677,19973,23833,26833,47933,73331,
%U A034302 74177,91733,93491,94397,111731,166931,333911,355933,477797,477977
%N A034302 Zeroless primes that remain prime if any digit is deleted.
%H A034302 Chai Wah Wu, <a href="/A034302/b034302.txt">Table of n, a(n) for n = 1..118</a> (terms 1..79 from T. D. Noe, terms 80..103 from Charles R Greathouse IV)
%H A034302 StackExchange, <a href="http://math.stackexchange.com/questions/33094">Deleting any digit yields a prime</a>
%t A034302 rpnzQ[n_]:=Module[{idn=IntegerDigits[n]},Count[idn,0]==0 && And@@ PrimeQ[FromDigits/@ Subsets[IntegerDigits[n], {Length[idn]-1}]]]; Select[Prime[Range[40000]],rpnzQ]  (* _Harvey P. Dale_, Mar 24 2011 *)
%o A034302 (Haskell)
%o A034302 import Data.List (inits, tails)
%o A034302 a034302 n = a034302_list !! (n-1)
%o A034302 a034302_list = filter f $ drop 4 a038618_list where
%o A034302    f x = all (== 1) $ map (a010051 . read) $
%o A034302              zipWith (++) (inits $ show x) (tail $ tails $ show x)
%o A034302 -- _Reinhard Zumkeller_, Dec 17 2011
%o A034302 (PARI) is(n)=my(d=digits(n),t=2^#d-1); if(vecmin(d)==0, return(0)); for(i=0,#d-1, if(!isprime(fromdigits(vecextract(d,t-2^i))), return(0))); isprime(n) \\ _Charles R Greathouse IV_, Jun 23 2017
%o A034302 (Python)
%o A034302 from itertools import product
%o A034302 from sympy import isprime
%o A034302 A034302_list, m = [23, 37, 53, 73], 7
%o A034302 for l in range(1,m-1): # generate all terms less than 10^m
%o A034302     for d in product('123456789',repeat=l):
%o A034302         for e in product('1379',repeat=2):
%o A034302             s = ''.join(d+e)
%o A034302             if isprime(int(s)):
%o A034302                 for i in range(len(s)):
%o A034302                     if not isprime(int(s[:i]+s[i+1:])):
%o A034302                         break
%o A034302                 else:
%o A034302                     A034302_list.append(int(s)) # _Chai Wah Wu_, Apr 05 2021
%Y A034302 Cf. A034303, A034304, A034305, A051362, A010051, A038618.
%K A034302 base,nonn,nice
%O A034302 1,1
%A A034302 _David W. Wilson_