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

1,1

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..44

Example

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

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

Prog

(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

Crossrefs

Cf. A053583, A077714, A077715, A077716.

Sequence in context: A105431 A360187 A053583 * A119723 A093011 A262147

Adjacent sequences: A077710 A077711 A077712 * A077714 A077715 A077716

Keyword

base,nonn

Author

Amarnath Murthy, Nov 19 2002

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

Status

approved