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A236671 Start with 8; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.

%I A236671 #21 May 22 2025 10:21:36
%S A236671 8,83,839,83911,839117,83911721,8391172123,83911721233,839117212337,
%T A236671 83911721233729,839117212337293,83911721233729399,839117212337293999,
%U A236671 83911721233729399993,839117212337293999931,83911721233729399993139
%N A236671 Start with 8; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.
%C A236671 a(n+1) is the next smallest prime beginning with a(n). Initial term is 8. After a(1), these are the primes arising in A069610.
%e A236671 a(1) = 8 by definition.
%e A236671 a(2) is the next smallest prime beginning with 8, so a(2) = 83.
%e A236671 a(3) is the next smallest prime beginning with 83, so a(3) = 839.
%t A236671 smp[n_]:=Module[{k=1},While[!PrimeQ[n*10^IntegerLength[k]+k],k++];n 10^IntegerLength[k]+ k]; NestList[smp,8,15] (* _Harvey P. Dale_, Aug 10 2024 *)
%o A236671 (Python)
%o A236671 import sympy
%o A236671 from sympy import isprime
%o A236671 def b(x):
%o A236671   num = str(x)
%o A236671   n = 1
%o A236671   while n < 10**3:
%o A236671     new_num = str(x) + str(n)
%o A236671     if isprime(int(new_num)):
%o A236671       print(int(new_num))
%o A236671       x = new_num
%o A236671       n = 1
%o A236671     else:
%o A236671       n += 1
%o A236671 b(8)
%Y A236671 Cf. A069610, A048553, A110773,
%K A236671 nonn,base
%O A236671 1,1
%A A236671 _Derek Orr_, Jan 29 2014