A236527 - OEIS

%I #18 Jun 22 2020 19:38:35

%S 3,31,311,3119,31193,3119317,31193171,311931713,3119317139,

%T 311931713939,31193171393933,3119317139393353,31193171393933531,

%U 3119317139393353121,311931713939335312127,311931713939335312127113,31193171393933531212711399,31193171393933531212711399123

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

%C a(n + 1) is the next smallest prime beginning with a(n). Initial term is 3. These are the primes arising in A069605.

%e a(1) = 3 by definition.

%e a(2) is the next smallest prime beginning with 3, so a(2) = 31.

%e a(3) is the next smallest prime beginning with 31, so a(3) = 311.

%t 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 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 (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(3)

%Y Cf. A048553, A110773, A069605.

%K nonn,base

%O 1,1

%A _Derek Orr_, Jan 27 2014