cp's OEIS Frontend

A034844 Primes with only nonprime decimal digits.

%I A034844 #55 Apr 03 2023 10:36:09
%S A034844 11,19,41,61,89,101,109,149,181,191,199,401,409,419,449,461,491,499,
%T A034844 601,619,641,661,691,809,811,881,911,919,941,991,1009,1019,1049,1061,
%U A034844 1069,1091,1109,1181,1409,1481,1489,1499,1601,1609,1619,1669,1699,1801,1811
%N A034844 Primes with only nonprime decimal digits.
%C A034844 A109066(n) = 0 iff prime(n) is in this sequence. [_Reinhard Zumkeller_, Jul 11 2010, corrected by _M. F. Hasler_, Aug 27 2012]
%C A034844 Or, primes p such that A193238(p) = 0. - _M. F. Hasler_, Aug 27 2012
%C A034844 Intersection of A084984 and A000040; complement of A179336 (within the primes A000040). [_Reinhard Zumkeller_, Jul 19 2011, edited by _M. F. Hasler_, Aug 27 2012]
%C A034844 The smallest prime that contains all the six nonprime decimal digits is a(694) = 104869 (see Prime Curios! link). - _Bernard Schott_, Mar 21 2023
%H A034844 T. D. Noe, <a href="/A034844/b034844.txt">Table of n, a(n) for n = 1..1000</a>
%H A034844 Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1,000 Primes</a>
%H A034844 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=104869">104869</a>, Prime Curios!
%F A034844 a(n) >> n^1.285. [_Charles R Greathouse IV_, Feb 20 2012]
%e A034844 E.g. 149 is a prime made of nonprime digits(1,4,9).
%e A034844 991 is a prime without any prime digits.
%t A034844 Select[Prime[Range[279]], Intersection[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* _Jayanta Basu_, Apr 18 2013 *)
%t A034844 Union[Select[Flatten[Table[FromDigits/@Tuples[{1,4,6,8,9,0},n],{n,2,4}]],PrimeQ]] (* _Harvey P. Dale_, Dec 08 2014 *)
%o A034844 (Haskell)
%o A034844 a034844 n = a034844_list !! (n-1)
%o A034844 a034844_list = filter (not . any  (`elem` "2357") . show ) a000040_list
%o A034844 -- _Reinhard Zumkeller_, Jul 19 2011
%o A034844 (Magma) [p: p in PrimesUpTo(2000) | forall{d: d in [2,3,5,7] | d notin Set(Intseq(p))}];  // _Bruno Berselli_, Jul 27 2011
%o A034844 (PARI) is_A034844(n)=isprime(n)&!apply(x->isprime(x),eval(Vec(Str(n)))) \\ _M. F. Hasler_, Aug 27 2012
%o A034844 (PARI) is_A034844(n)=isprime(n)&!setintersect(Set(Vec(Str(n))),Vec("2357")) \\ _M. F. Hasler_, Aug 27 2012
%o A034844 (Python)
%o A034844 from sympy import isprime
%o A034844 from itertools import product
%o A034844 def auptod(maxdigits):
%o A034844     alst = []
%o A034844     for d in range(1, maxdigits+1):
%o A034844         for p in product("014689", repeat=d-1):
%o A034844             if d > 1 and p[0] == "0": continue
%o A034844             for end in "19":
%o A034844                 s = "".join(p) + end
%o A034844                 t = int(s)
%o A034844                 if isprime(t): alst.append(t)
%o A034844     return alst
%o A034844 print(auptod(4)) # _Michael S. Branicky_, Nov 19 2021
%Y A034844 Cf. A000040, A084984.
%Y A034844 Cf. A033274, A109066, A152313, A141409.
%K A034844 nonn,base
%O A034844 1,1
%A A034844 _Erich Friedman_
%E A034844 Edited by _N. J. A. Sloane_, Feb 22 2009 at the suggestion of _R. J. Mathar_