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

11, 101, 11411, 100411, 101141, 114001, 114041, 140411, 141101, 1004141, 1010411, 1040141, 1041041, 1100441, 1114111, 1140101, 1144441, 1401401, 1410401, 1411141, 1414001, 1440011, 1444411, 1444441, 10010411, 10011101, 10041011, 10044011

Offset: 1

Author

M. F. Hasler, Nov 04 2011

Keywords

• nonn
• base

Comments

All terms start and end with the digit 1.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.

Programs

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

Maple

F:= proc(d) local A0, A4, Res, q, r;
   Res:= NULL;
   q:= (10^(d+1)-1)/9;
   for A0 in combinat:-powerset({$1..d-1}) do
     for A4 in combinat:-powerset({$1..d-1} minus A0) do
       r:= q - add(10^i,i=A0) + 3*add(10^i,i=A4);
       if isprime(r) and isprime(q - add(10^(d-i),i=A0) + 3*add(10^(d-i),i=A4)) then
          Res:= Res, r
       fi
   od od;
   Res
end proc:
sort([seq(F(d),d=1..7)]); # Robert Israel, May 03 2018

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 */

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