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

3, 31, 311, 3119, 31193, 3119317, 31193171, 311931713, 3119317139, 311931713939, 31193171393933, 3119317139393353, 31193171393933531, 3119317139393353121, 311931713939335312127, 311931713939335312127113, 31193171393933531212711399, 31193171393933531212711399123

Offset: 1

Author

Derek Orr, Jan 27 2014

Keywords

• nonn
• base

Comments

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

Examples

			a(1) = 3 by definition.
a(2) is the next smallest prime beginning with 3, so a(2) = 31.
a(3) is the next smallest prime beginning with 31, so a(3) = 311.
		

Crossrefs

Cf. A048553, A110773, A069605.

Programs

Mathematica

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 *)
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 *)

Python

import sympy
from sympy import isprime
def b(x):
  num = str(x)
  n = 1
  while n < 10**3:
    new_num = str(x) + str(n)
    if isprime(int(new_num)):
      print(int(new_num))
      x = new_num
      n = 1
    else:
      n += 1
b(3)