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

1,1

Comments

All terms start and end with the digit 1.

Links

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

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A020449 A089971 A082620 * A156668 A103992 A185949

Adjacent sequences: A199301 A199302 A199303 * A199305 A199306 A199307

Keyword

nonn,base

Author

M. F. Hasler, Nov 04 2011

Status

approved