A380010 Beginning with 7, least prime such that concatenation of the first n terms is prime.

7, 3, 3, 3, 31, 23, 13, 3, 167, 13, 137, 3, 73, 383, 499, 431, 13, 101, 61, 47, 67, 101, 13, 83, 1237, 107, 97, 467, 499, 677, 1423, 353, 73, 431, 331, 683, 487, 2141, 3, 1753, 1787, 31, 443, 139, 653, 1327, 17, 919, 173, 2851, 137, 547, 557, 5167, 347, 7867, 839, 19, 179, 19

Offset: 1

Author

J.W.L. (Jan) Eerland, Jan 09 2025

Keywords

• base
• nonn

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A111382, A111383, A113584, A379354, A379355, A379761, A380011.

Programs

Mathematica

w={7};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,2,50}];w

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    s, an = "", 7
    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(), 50))) # after Michael S. Branicky in A379354