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A376500 Primes that contain at least one even digit and two different odd digits where any permutation of the odd digits leaving the even digits fixed produces a prime.

%I A376500 #17 Oct 23 2024 16:32:26
%S A376500 107,149,167,239,293,347,389,419,491,613,619,631,691,701,709,743,761,
%T A376500 769,907,941,967,983,1009,1013,1019,1031,1049,1063,1091,1123,1223,
%U A376500 1229,1249,1289,1321,1429,1487,1499,1609,1627,1669,1823,1847,2113,2131,2143,2237,2239,2273,2293,2309,2311,2341
%N A376500 Primes that contain at least one even digit and two different odd digits where any permutation of the odd digits leaving the even digits fixed produces a prime.
%C A376500 The primes in the sequence cannot contain 5.
%H A376500 Robert Israel, <a href="/A376500/b376500.txt">Table of n, a(n) for n = 1..10000</a>
%e A376500 1013 is a term since the permutations of the odd digits that leave the even digits fixed give 1031 and 3011, which are also prime.
%p A376500 filter:= proc(n) local L,oddi,eveni,xeven,i;
%p A376500  if not isprime(n) then return false fi;
%p A376500  L:= convert(n,base,10);
%p A376500  if member(5,L) then return false fi;
%p A376500  oddi,eveni:= selectremove(t -> L[t]::odd,[$1..nops(L)]);
%p A376500  if nops(eveni) = 0 or nops(convert(L[oddi],set))<2 then return false fi;
%p A376500  xeven:= add(10^(i-1)*L[i],i=eveni);
%p A376500  andmap(t -> isprime(xeven+add(10^(oddi[i]-1)*L[t[i]],i=1..nops(oddi))), combinat:-permute(oddi))
%p A376500 end proc:
%p A376500 select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Oct 23 2024
%Y A376500 Cf. A000040, A003459, A376501, A376502.
%K A376500 nonn,base
%O A376500 1,1
%A A376500 _Enrique Navarrete_, Sep 25 2024