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%I #17 Jul 20 2024 13:23:18
%S 4,41,419,41911,4191119,41911193,419111933,41911193341,4191119334151,
%T 419111933415151,41911193341515187,4191119334151518719,
%U 419111933415151871963,41911193341515187196323,4191119334151518719632313,419111933415151871963231329
%N Start with 4; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.
%C a(n+1) is the next smallest prime beginning with a(n). Initial term is 4.
%C After a(1), these are the primes arising in A069606.
%e a(1) = 4 by definition.
%e a(2) is the next smallest prime beginning with 4, so a(2) = 41.
%e a(3) is the next smallest prime beginning with 41, so a(3) = 419.
%e ...and so on.
%t NestList[Module[{k=1},While[!PrimeQ[#*10^IntegerLength[k]+k],k+=2];#*10^IntegerLength[k]+ k]&,4,20] (* _Harvey P. Dale_, Jul 20 2024 *)
%o (Python)
%o import sympy
%o from sympy import isprime
%o def b(x):
%o ..num = str(x)
%o ..n = 1
%o ..while n < 10**3:
%o ....new_num = str(x) + str(n)
%o ....if isprime(int(new_num)):
%o ......print(int(new_num))
%o ......x = new_num
%o ......n = 1
%o ....else:
%o ......n += 1
%o b(4)
%Y Cf. A110773, A048553, A069606.
%K nonn,base
%O 1,1
%A _Derek Orr_, Jan 27 2014