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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A057876 A244282 A051362 * A057878 A019549 A272157
KEYWORD
base,nonn,nice
AUTHOR
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)