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A034302
Zeroless primes that remain prime if any digit is deleted.
15
23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1499, 1997, 2239, 2293, 3137, 4919, 6173, 7433, 9677, 19973, 23833, 26833, 47933, 73331, 74177, 91733, 93491, 94397, 111731, 166931, 333911, 355933, 477797, 477977
OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..118 (terms 1..79 from T. D. Noe, terms 80..103 from Charles R Greathouse IV)
MATHEMATICA
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 *)
PROG
(Haskell)
import Data.List (inits, tails)
a034302 n = a034302_list !! (n-1)
a034302_list = filter f $ drop 4 a038618_list where
f x = all (== 1) $ map (a010051 . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x)
-- Reinhard Zumkeller, Dec 17 2011
(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
(Python)
from itertools import product
from sympy import isprime
A034302_list, m = [23, 37, 53, 73], 7
for l in range(1, m-1): # generate all terms less than 10^m
for d in product('123456789', repeat=l):
for e in product('1379', repeat=2):
s = ''.join(d+e)
if isprime(int(s)):
for i in range(len(s)):
if not isprime(int(s[:i]+s[i+1:])):
break
else:
A034302_list.append(int(s)) # Chai Wah Wu, Apr 05 2021
CROSSREFS
KEYWORD
base,nonn,nice
STATUS
approved