A379355 Beginning with 3, least prime such that the reversal concatenation of first n terms is prime.

3, 2, 2, 13, 2, 13, 59, 31, 263, 73, 23, 31, 449, 31, 59, 313, 2, 3, 211, 317, 31, 449, 241, 887, 349, 911, 853, 887, 313, 173, 1777, 179, 967, 503, 331, 113, 163, 359, 1153, 281, 97, 1823, 13, 23, 1657, 269, 223, 3623, 2017, 233, 61, 1361, 367, 1031, 79, 389, 577, 2963, 1741, 59, 13, 1439, 463, 797

Offset: 1

Author

J.W.L. (Jan) Eerland, Dec 21 2024

Keywords

• base
• nonn

Comments

"Reverse concatenation" here seems to refer to the decimal concatenation R(a(n)) || R(a(n-1)) || ... || R(a(3)) || R(a(2)) || R(a(1)) where R(k) means "reverse digits of k". - N. J. A. Sloane, Jan 03 2025

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A111382, A111383, A113584, A379354.

The primes produced are in A379782.

Programs

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]]]]]]], Break[]]; k++];
     Prime[k]], k];
  w = Append[w, q], {i, 2, 57}];
w

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    r, an = "", 3
    while True:
        yield int(an)
        r = digits(an)[::-1] + r
        p = 2
        while not is_prime(mpz(digits(p)[::-1]+r)): p = next_prime(p)
        an = p
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 21 2024