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A199304 Palindromic primes in the sense of A007500 with digits '0', '1' and '4' only. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 14 16:05 EDT 2020. Contains 335729 sequences. (Running on oeis4.)