A382898 Beginning with 13, least prime such that concatenation of first n terms and its digit reversal both are primes.

13, 151, 227, 2083, 887, 79, 2963, 1579, 6287, 1321, 6719, 54919, 26699, 8647, 4229, 3919, 102161, 42433, 1667, 192193, 11633, 186343, 47339, 3259, 65963, 14293, 29717, 61297, 28493, 231367, 43793, 145021, 566441, 475903, 92381, 80473, 139967, 882061, 72893, 709279, 6053, 114487, 1179389, 204331, 203351, 139831, 396239, 205327, 501173, 951589

Offset: 1

Author

J.W.L. (Jan) Eerland, Apr 08 2025

Keywords

• base
• nonn

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A113584 (same for 3), A379761 (same for 7), A380227 (same for 11).

Cf. A111382, A111383, A379354, A379355.

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:= 13: x:= 13:
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; # after Robert Israel in A113584

Mathematica

w={13};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]],{i,k}];w=Append[w,q],{i,2,50}];w

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    s, r, an = "", "", 13
    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(), 40))) # after Michael S. Branicky in A113584