OFFSET
1,1
COMMENTS
This sequence is infinite by the Prime Number Theorem. - Charles R Greathouse IV, Apr 09 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ≍ n log n. The ratio a(n)/(n log n) is bounded but does not have a limit. - Charles R Greathouse IV, Apr 09 2024
MAPLE
R:= NULL: count:= 0:
for d from 0 while count < 100 do
for a from 1 to 9 while count < 100 do
for b from 1 to 10^d-1 by 2 while count < 100 do
x:= b + 10^d*(2345 + 10000*a);
if isprime(x) then
count:= count+1; R:= R, x
fi
od od od:
R;
MATHEMATICA
p = 12345; s = {}; Do[p = NextPrime[p];
If[2 == IntegerDigits[p][[2]] && 3 == IntegerDigits[p][[3]] && 4 ==IntegerDigits[p][[4]] && 5 == IntegerDigits[p][[5]], AppendTo[s, p]],
{1000000}]; s
PROG
(Python)
from itertools import count, islice
from sympy import primerange
def A371845_gen(): # generator of terms
for l in count(1):
m = 10**l
for a in range(1, 10):
b = (a*10**4+2345)*m
yield from primerange(b, b+m)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zak Seidov and Robert Israel, Apr 08 2024
STATUS
approved