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

1,1

Links

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

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

Prog

(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

Crossrefs

Cf. A111382, A111383, A113584, A379355.

Sequence in context: A066065 A145511 A242461 * A065443 A388694 A198350

Adjacent sequences: A379351 A379352 A379353 * A379355 A379356 A379357

Keyword

base,nonn

Author

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

Status

approved