OFFSET
1,1
COMMENTS
Number of primes of the form: ... ddd3ddd2ddd1ddd0 = ddd0 * 10^0 + ddd1 * 10^3 + ddd2 * 10^6 + ddd3 * 10^9 + ..., where ddd0, ddd1, ddd2, ddd3, ... are prime with 3 digits. The i-th element of the sequence is the number of primes with i * 3 digits.
Approximation for the sum of the sequence up to a(k) for large values of k: Sum_{i=1..k} a(i) = 10^(3*k) / (3*k*log(10)) * (143/1000)^(k-1).
EXAMPLE
Example: a(2) = 2753 because there are 2753 numbers of the form ddd1ddd0 with ddd0, ddd1 prime numbers, i.e.: 101107, 101113, 101149, 101173, 101197, 101281, 101293, ..., 997991.
PROG
(Python)
from itertools import product
from sympy import isprime, primerange
def a(n):
p3 = list(map(str, primerange(100, 1000)))
return sum(1 for p in product(p3, repeat=n) if isprime(int("".join(p))))
print([a(n) for n in range(1, 4)]) # Michael S. Branicky, Feb 13 2023
CROSSREFS
KEYWORD
nonn,base,bref
AUTHOR
Giorgio Balzarotti & Paolo P. Lava, Dec 07 2007
EXTENSIONS
a(4) from Donovan Johnson, Apr 17 2010
a(5) from Michael S. Branicky, Feb 13 2023
STATUS
approved