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A077716
a(1) = 19; 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.
4
19, 419, 5419, 35419, 435419, 80435419, 30000080435419, 1030000080435419, 91030000080435419, 20091030000080435419, 720091030000080435419, 50720091030000080435419, 650720091030000080435419, 10650720091030000080435419, 2000000010650720091030000080435419
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..51
MAPLE
a:= proc(n) option remember; local k, m, d, p;
if n=1 then 19 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=19):
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(), 15))) # Michael S. Branicky, Jun 23 2022
CROSSREFS
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