A077713 a(1) = 3; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.

3, 13, 113, 2113, 12113, 612113, 50612113, 1050612113, 6001050612113, 26001050612113, 1026001050612113, 6000001026001050612113, 500006000001026001050612113, 600500006000001026001050612113, 1600500006000001026001050612113, 6001600500006000001026001050612113

Offset: 1

Author

Amarnath Murthy, Nov 19 2002

Keywords

• base
• nonn

Comments

a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.

Examples

			a(7) = 50612113: deleting 5 gives 612113 = a(6).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A053583, A077714, A077715, A077716.

Programs

Maple

a:= proc(n) option remember; local k, m, d, p;
      if n=1 then 3 else k:= a(n-1);
        for m from length(k) do
          for d to 9 do p:= k +d*10^m;
            if isprime(p) then return p fi
        od od
      fi
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 12 2015

Python

from sympy import isprime
from itertools import islice
def agen(an=3):
    while True:
        yield an
        pow10 = 10**len(str(an))
        while True:
            found = False
            for t in range(pow10+an, 10*pow10+an, pow10):
                if isprime(t):
                    an = t; found = True; break
            if found: break
            pow10 *= 10
print(list(islice(agen(), 16))) # Michael S. Branicky, Jun 23 2022

Extensions

More terms from Ray Chandler, Jul 23 2003

Changed offset to 1 by Alois P. Heinz, Jan 12 2015

Definition clarified by N. J. A. Sloane, Jan 19 2015