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Primes which have an even decimal digit and remain prime after all even digits are removed.
3

%I #15 Jul 04 2018 05:49:19

%S 23,43,47,67,83,101,103,107,109,127,149,163,167,181,211,223,227,263,

%T 271,283,307,347,367,419,431,443,463,467,479,487,503,509,523,563,569,

%U 607,613,617,619,631,643,647,653,659,673,683,701,709,743,761,769,811,823,827,853,859,863,883,887,907

%N Primes which have an even decimal digit and remain prime after all even digits are removed.

%C A proper subset of A306084.

%H Robert Israel, <a href="/A306085/b306085.txt">Table of n, a(n) for n = 1..10000</a>

%e 101 is a member of the sequence because it has an even digit, 0, and with its removal, the resulting number 11 is a prime.

%p filter:= proc(n) local L,Lp;

%p if not isprime(n) then return false fi;

%p L:= convert(n,base,10);

%p Lp:= subs([0=NULL,2=NULL,4=NULL,6=NULL,8=NULL],L);

%p if L = Lp then return false fi;

%p isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp)))

%p end proc:

%p select(filter, [seq(n,n=11..1000,2)]); # _Robert Israel_, Jul 04 2018

%t fQ[n_] := Block[{id = IntegerDigits@ n}, Select[id, EvenQ] != {} && PrimeQ[ FromDigits[ Select[id, OddQ]] ]]; Select[Prime@ Range@ 160, fQ]

%o (PARI) isok(p) = isprime(p) && (d=digits(p)) && #select(x->!(x%2), d) && isprime(fromdigits(select(x->(x % 2), d))); \\ _Michel Marcus_, Jun 22 2018

%Y Cf. A306084, A306086.

%K nonn,base

%O 1,1

%A _Zak Seidov_ and _Robert G. Wilson v_, Jun 20 2018