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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.
4
107, 149, 167, 239, 293, 347, 389, 419, 491, 613, 619, 631, 691, 701, 709, 743, 761, 769, 907, 941, 967, 983, 1009, 1013, 1019, 1031, 1049, 1063, 1091, 1123, 1223, 1229, 1249, 1289, 1321, 1429, 1487, 1499, 1609, 1627, 1669, 1823, 1847, 2113, 2131, 2143, 2237, 2239, 2273, 2293, 2309, 2311, 2341
OFFSET
1,1
COMMENTS
The primes in the sequence cannot contain 5.
LINKS
EXAMPLE
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.
MAPLE
filter:= proc(n) local L, oddi, eveni, xeven, i;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
if member(5, L) then return false fi;
oddi, eveni:= selectremove(t -> L[t]::odd, [$1..nops(L)]);
if nops(eveni) = 0 or nops(convert(L[oddi], set))<2 then return false fi;
xeven:= add(10^(i-1)*L[i], i=eveni);
andmap(t -> isprime(xeven+add(10^(oddi[i]-1)*L[t[i]], i=1..nops(oddi))), combinat:-permute(oddi))
end proc:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Oct 23 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Enrique Navarrete, Sep 25 2024
STATUS
approved