cp's OEIS Frontend

A199304 Palindromic primes in the sense of A007500 with digits '0', '1' and '4' only.

%I A199304 #20 Sep 08 2022 08:46:00
%S A199304 11,101,11411,100411,101141,114001,114041,140411,141101,1004141,
%T A199304 1010411,1040141,1041041,1100441,1114111,1140101,1144441,1401401,
%U A199304 1410401,1411141,1414001,1440011,1444411,1444441,10010411,10011101,10041011,10044011
%N A199304 Palindromic primes in the sense of A007500 with digits '0', '1' and '4' only.
%C A199304 All terms start and end with the digit 1.
%H A199304 Robert Israel, <a href="/A199304/b199304.txt">Table of n, a(n) for n = 1..10000</a>
%p A199304 F:= proc(d) local A0, A4, Res, q, r;
%p A199304    Res:= NULL;
%p A199304    q:= (10^(d+1)-1)/9;
%p A199304    for A0 in combinat:-powerset({$1..d-1}) do
%p A199304      for A4 in combinat:-powerset({$1..d-1} minus A0) do
%p A199304        r:= q - add(10^i,i=A0) + 3*add(10^i,i=A4);
%p A199304        if isprime(r) and isprime(q - add(10^(d-i),i=A0) + 3*add(10^(d-i),i=A4)) then
%p A199304           Res:= Res, r
%p A199304        fi
%p A199304    od od;
%p A199304    Res
%p A199304 end proc:
%p A199304 sort([seq(F(d),d=1..7)]); # _Robert Israel_, May 03 2018
%o A199304 (PARI) allow=Vec("014");forprime(p=1,default(primelimit),setminus( Set( Vec(Str( p ))),allow)&next;isprime(A004086(p))&print1(p",")) /* better use the more efficient code below */
%o A199304 (PARI) a(n=50,list=0,L=[0,1,4],needpal=1)={ for(d=1,1e9, u=vector(d,i,10^(d-i))~; forvec(v=vector(d,i,[1+(i==1&!L[1]),#L]), isprime(t=vector(d,i,L[v[i]])*u) || next; needpal & !isprime(A004086(t)) & next; list & print1(t","); n-- || return(t)))}  \\ _M. F. Hasler_, Nov 06 2011
%o A199304 (Magma) [p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0,1,4] and IsPrime(Seqint(Reverse(Intseq(p))))];  // _Bruno Berselli_, Nov 07 2011
%Y A199304 Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.
%K A199304 nonn,base
%O A199304 1,1
%A A199304 _M. F. Hasler_, Nov 04 2011