A379354 Beginning with 3, least prime such that concatenation of first n terms is prime.

3, 7, 3, 3, 7, 29, 43, 11, 61, 71, 19, 191, 43, 53, 7, 239, 31, 173, 43, 137, 79, 53, 13, 557, 619, 47, 271, 797, 463, 83, 211, 467, 229, 131, 199, 359, 1249, 887, 853, 641, 109, 257, 1153, 1031, 613, 953, 607, 641, 499, 359, 1297, 1031, 2137, 401, 283, 29, 1321, 1499, 547, 83, 397, 2153, 1759, 1277

Offset: 1

Author

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

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A111382, A111383, A113584, A379355.

Programs

Mathematica

w = {3};
Do[k = 1;
  q = Monitor[
    Parallelize[
     While[True,
      If[PrimeQ[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
    s, an = "", 3
    while True:
        yield int(an)
        s += digits(an)
        p = 3
        while not is_prime(mpz(s+digits(p))): p = next_prime(p)
        an = p
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 21 2024