A077715 a(1) = 7; 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.

7, 17, 317, 6317, 26317, 126317, 2126317, 72126317, 372126317, 5372126317, 305372126317, 9305372126317, 409305372126317, 20409305372126317, 100020409305372126317, 9100020409305372126317, 209100020409305372126317, 40209100020409305372126317

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.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A053584, A077713, A077714, A077716.

Programs

Maple

a:= proc(n) option remember; local k, m, d, p;
      if n=1 then 7 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=7):
    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(), 18))) # Michael S. Branicky, Jun 23 2022

Extensions

More terms from Ray Chandler, Jul 23 2003

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