A113584 Beginning with 3, least prime such that concatenation of first n terms and its digit reversal both are primes.

3, 7, 3, 3, 43, 101, 19, 269, 1873, 41, 241, 3137, 139, 9011, 9187, 641, 29881, 12227, 3169, 13499, 8539, 7019, 19447, 12899, 73243, 124769, 1063, 37847, 127, 32321, 104287, 3407, 93553, 256643, 165469, 744659, 60217, 54773, 49297, 214457, 314077, 271409, 602383, 56921, 193051, 255383, 75991, 25667, 583147, 121019

Offset: 1

Author

Amarnath Murthy, Nov 06 2005

Keywords

• base
• nonn

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..224

Crossrefs

Cf. A111382, A111383.

Programs

Maple

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
tcat:= proc(a,b)
  a*10^(1+ilog10(b))+b
end proc:
A:= 3: x:= 3:
for i from 1 to 50 do
   p:= 2:
   do
     p:= nextprime(p);
     y:= tcat(x,p);
     if isprime(y) and isprime(rev(y)) then
          A:= A,p;
          x:= y;
          break
     fi;
   od
od:
A; # Robert Israel, Dec 26 2024

Mathematica

w = {3};
Do[k = 1;
  q = Monitor[
    Parallelize[
     While[True,
      If[PrimeQ[
         FromDigits[
          Join @@ IntegerDigits /@
            Reverse[
             IntegerDigits[
              FromDigits[
               Join @@ IntegerDigits /@ Append[w, Prime[k]]]]]]] &&
        PrimeQ[FromDigits[
          Join @@ IntegerDigits /@ Append[w, Prime[k]]]], Break[]]; k++];
     Prime[k]], k];
  w = Append[w, q], {i, 2, 50}];
w (* J.W.L. (Jan) Eerland, Dec 19 2024 *)

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    s, r, an = "", "", 3
    while True:
        yield int(an)
        d = digits(an)
        s, r, p, sp = s+d, d[::-1]+r, 3, "3"
        while not is_prime(mpz(s+sp)) or not is_prime(mpz(sp[::-1]+r)):
            p = next_prime(p)
            sp = digits(p)
        an = p
print(list(islice(agen(), 50))) # Michael S. Branicky, Jan 02 2025

Extensions

Corrected and extended by Hans Havermann, Nov 08 2005

a(40)-a(50) from J.W.L. (Jan) Eerland, Dec 19 2024