A236528 Start with 4; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.

4, 41, 419, 41911, 4191119, 41911193, 419111933, 41911193341, 4191119334151, 419111933415151, 41911193341515187, 4191119334151518719, 419111933415151871963, 41911193341515187196323, 4191119334151518719632313, 419111933415151871963231329

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 4.

After a(1), these are the primes arising in A069606.

Examples

			a(1) = 4 by definition.
a(2) is the next smallest prime beginning with 4, so a(2) = 41.
a(3) is the next smallest prime beginning with 41, so a(3) = 419.
...and so on.
		

Crossrefs

Cf. A110773, A048553, A069606.

Programs

Mathematica

NestList[Module[{k=1},While[!PrimeQ[#*10^IntegerLength[k]+k],k+=2];#*10^IntegerLength[k]+ k]&,4,20] (* Harvey P. Dale, Jul 20 2024 *)

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(4)