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

%I A380010 #19 Jan 18 2025 14:46:40
%S A380010 7,3,3,3,31,23,13,3,167,13,137,3,73,383,499,431,13,101,61,47,67,101,
%T A380010 13,83,1237,107,97,467,499,677,1423,353,73,431,331,683,487,2141,3,
%U A380010 1753,1787,31,443,139,653,1327,17,919,173,2851,137,547,557,5167,347,7867,839,19,179,19
%N A380010 Beginning with 7, least prime such that concatenation of the first n terms is prime.
%H A380010 J.W.L. (Jan) Eerland, <a href="/A380010/b380010.txt">Table of n, a(n) for n = 1..1000</a>
%t A380010 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
%o A380010 (Python)
%o A380010 from itertools import count, islice
%o A380010 from gmpy2 import digits, is_prime, mpz, next_prime
%o A380010 def agen(): # generator of terms
%o A380010     s, an = "", 7
%o A380010     while True:
%o A380010         yield int(an)
%o A380010         s += digits(an)
%o A380010         p = 3
%o A380010         while not is_prime(mpz(s+digits(p))): p = next_prime(p)
%o A380010         an = p
%o A380010 print(list(islice(agen(), 50))) # after _Michael S. Branicky_ in A379354
%Y A380010 Cf. A111382, A111383, A113584, A379354, A379355, A379761, A380011.
%K A380010 base,nonn
%O A380010 1,1
%A A380010 _J.W.L. (Jan) Eerland_, Jan 09 2025