A077714 a(1) = 1; 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.

1, 11, 211, 4211, 34211, 234211, 4234211, 304234211, 9304234211, 209304234211, 7209304234211, 37209304234211, 3037209304234211, 23037209304234211, 323037209304234211, 70000323037209304234211, 300070000323037209304234211, 600300070000323037209304234211

Offset

1,2

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

Alois P. Heinz, Table of n, a(n) for n = 1..52

Example

a(8) = 304234211; deleting 3 gives 4234211 = a(7).

Maple

a:= proc(n) option remember; local k, m, d, p;
      if n=1 then 1 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

Prog

(Python)
from sympy import isprime
from itertools import islice
def agen(an=1):
    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

Crossrefs

Cf. A053582, A077713, A077715, A077716.

Sequence in context: A038399 A053547 A053582 * A089567 A110747 A112704

Adjacent sequences: A077711 A077712 A077713 * A077715 A077716 A077717

Keyword

base,nonn

Author

Amarnath Murthy, Nov 19 2002

Extensions

More terms from Ray Chandler, Jul 23 2003

Offset changed to 1 by Alois P. Heinz, Jan 12 2015

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

Status

approved