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