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

1,1

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..50

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

Prog

(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

Crossrefs

Cf. A053584, A077713, A077714, A077716.

Sequence in context: A110120 A201305 A053584 * A089563 A159028 A102266

Adjacent sequences: A077712 A077713 A077714 * A077716 A077717 A077718

Keyword

base,nonn

Author

Amarnath Murthy, Nov 19 2002

Extensions

More terms from Ray Chandler, Jul 23 2003

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

Status

approved