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A323391 Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.

%I A323391 #38 Feb 12 2019 04:15:26
%S A323391 19,41,61,89,149,419,461,491,619,641,691,941,1489,4691,4861,6481,6491,
%T A323391 6841,8419,8461,8641,8941,9461,14869,46819,48619,49681,64189,64891,
%U A323391 68491,69481,81649,84691,84961,86491,98641
%N A323391 Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.
%C A323391 There are only 36 terms in this sequence, which is a finite subsequence of A152313.
%C A323391 Two particular examples:
%C A323391 6481 is also the smallest prime formed from the concatenation of two consecutive squares.
%C A323391 81649 is the only prime containing all the nonprime positive digits such that every string of two consecutive digits is a square.
%H A323391 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=81649">81649</a>, Prime Curios!
%e A323391 14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.
%t A323391 Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* _Michael De Vlieger_, Jan 19 2019 *)
%o A323391 (PARI) isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ _Michel Marcus_, Jan 14 2019
%Y A323391 Subsequence of A152313. Subsequence of A029743. Subsequence of A155024 (with distinct nonprime digits but with 0) and of A034844.
%Y A323391 Cf. A029743 (with distinct digits), A124674 (with distinct prime digits), A155045 (with distinct odd digits), A323387 (with distinct square digits), A323578 (with distinct digits for which parity of digits alternates).
%K A323391 nonn,base,fini,full
%O A323391 1,1
%A A323391 _Bernard Schott_, Jan 13 2019