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A236527 Primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime, starting with 3.

%I A236527 #20 May 22 2025 10:21:36
%S A236527 3,31,311,3119,31193,3119317,31193171,311931713,3119317139,
%T A236527 311931713939,31193171393933,3119317139393353,31193171393933531,
%U A236527 3119317139393353121,311931713939335312127,311931713939335312127113,31193171393933531212711399,31193171393933531212711399123
%N A236527 Primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime, starting with 3.
%C A236527 a(n + 1) is the next smallest prime beginning with a(n). Initial term is 3. These are the primes arising in A069605.
%e A236527 a(1) = 3 by definition.
%e A236527 a(2) is the next smallest prime beginning with 3, so a(2) = 31.
%e A236527 a(3) is the next smallest prime beginning with 31, so a(3) = 311.
%t A236527 A069605[1] = 3; A236527[1] = 3; A069605[n_] := A069605[n] = Block[{k = 1, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits[Flatten[Append[c, IntegerDigits[k]]]]], k += 2]; k]; A236527[n_] := A236527[n] = FromDigits[Flatten[IntegerDigits[A236527[n - 1]], IntegerDigits[A069605[n]]]]; Table[A236527[n], {n, 20}] (* _Alonso del Arte_, Jan 28 2014 based on _Robert G. Wilson v_'s program for A069605 *)
%t A236527 nxt[n_]:=Module[{s=1},While[CompositeQ[n*10^IntegerLength[s]+s],s+=2];n*10^IntegerLength[s]+s]; NestList[nxt,3,20] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 22 2020 *)
%o A236527 (Python)
%o A236527 import sympy
%o A236527 from sympy import isprime
%o A236527 def b(x):
%o A236527   num = str(x)
%o A236527   n = 1
%o A236527   while n < 10**3:
%o A236527     new_num = str(x) + str(n)
%o A236527     if isprime(int(new_num)):
%o A236527       print(int(new_num))
%o A236527       x = new_num
%o A236527       n = 1
%o A236527     else:
%o A236527       n += 1
%o A236527 b(3)
%Y A236527 Cf. A048553, A110773, A069605.
%K A236527 nonn,base
%O A236527 1,1
%A A236527 _Derek Orr_, Jan 27 2014