A236672 Start with 9; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.

9, 97, 971, 9719, 971917, 97191713, 9719171333, 971917133323, 9719171333237, 971917133323777, 97191713332377731, 9719171333237773159, 971917133323777315951, 97191713332377731595127, 971917133323777315951277, 971917133323777315951277269

Offset: 1

Author

Derek Orr, Jan 29 2014

Keywords

• nonn
• base

Comments

a(n+1) is the next smallest prime beginning with a(n). Initial term is 9. After a(1), these are the primes in A069611.

Examples

			a(1) = 9 by definition.
a(2) is the next smallest prime beginning with 9, so a(2) = 97.
a(3) is the next smallest prime beginning with 97, so a(3) = 971.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..316

Crossrefs

Cf. A048553, A110773, A069611.

Programs

Maple

R:= 9: x:= 9:
for i from 2 to 20 do
  for y from 1 by 2 do
    z:= x*10^(1+ilog10(y)) + y;
    if isprime(z) then
      R:= R,z; x:= z; break
    fi
od od:
R; # Robert Israel, Nov 22 2023

Mathematica

next[p_]:=Module[{i=1,q},While[!PrimeQ[q=10^IntegerLength[i]p+i],i+=2];q];
NestList[next,9,15] (* Paolo Xausa, Nov 23 2023 *)

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(9)