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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A111382, A111383.

Sequence in context: A198350 A117190 A375553 * A111383 A195769 A021968

Adjacent sequences: A113581 A113582 A113583 * A113585 A113586 A113587

Keyword

base,nonn

Author

Amarnath Murthy, Nov 06 2005

Extensions

Corrected and extended by Hans Havermann, Nov 08 2005

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

Status

approved