cp's OEIS Frontend

A244529 Prime numbers whose decimal expansion contains no repeated digits or zeros, whose digits cannot be rearranged to form another prime number.

%I A244529 #41 Nov 10 2024 02:23:23
%S A244529 2,3,5,7,19,23,29,41,43,47,53,59,61,67,83,89,257,263,269,431,487,523,
%T A244529 541,827,829,853,859,2861,5623,5849
%N A244529 Prime numbers whose decimal expansion contains no repeated digits or zeros, whose digits cannot be rearranged to form another prime number.
%C A244529 There are only thirty prime numbers which meet the criteria.
%C A244529 The largest prime in this sequence happens, as noted by _Farideh Firoozbakht_, to have the property pi(5849) = (pi(5)*pi(8)*pi(4)*pi(9)) * (pi(pi(5))*pi(pi(8))*pi(pi(4))*pi(pi(9))), where pi = A000720. Note that 5849 is the earliest multi-digit prime with this property. - _Jonathan Vos Post_, Jun 30 2014
%H A244529 Prime Curios, <a href="https://t5k.org/curios/page.php?short=5849">5849</a>
%e A244529 541 (prime) -> 145, 154, 415, 451, 514 (all nonprime).
%p A244529 with(combinat):
%p A244529 T:= n-> sort(map(h-> h[], select(z-> nops(z)=1,
%p A244529     map(x-> map(y-> select(isprime, parse(cat(y[]))),
%p A244529     permute(x)), choose([$1..9], n)))))[]:
%p A244529 seq(T(n), n=1..4);  # _Alois P. Heinz_, Jun 29 2014
%t A244529 nrdQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&Length[Union[idn]] == Length[idn]&&Count[FromDigits/@Permutations[idn],_?PrimeQ]==1]; Select[ Prime[ Range[800]],nrdQ] (* _Harvey P. Dale_, Apr 27 2018 *)
%Y A244529 Cf. A000720.
%K A244529 nonn,base,fini,full
%O A244529 1,1
%A A244529 _Andreas Boe_, Jun 29 2014