OFFSET
1,1
COMMENTS
Number of primes of the form: .. dd3dd2dd1dd0 = dd0 * 10^0 + dd1 * 10^2 + dd2 * 10^4 + dd3 * 10^6 + ..., where dd0, dd1, dd2, dd3, ... are primes with two digits. The i-th element of the sequence is the number of primes with i * 2 digits.
Approximation for the sum of the sequence up to a(k) for large values of k: Sum_{i=1..k} a(i) = 10^(2*k) / (2*k*log(10)) * (21/100)^(k-1).
EXAMPLE
a(2) = 80 because there are 80 numbers of the form dd1dd0 with dd0, dd1 prime numbers of 2 digits, i.e.: 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, ..., 9767.
PROG
(Python)
from itertools import product
from sympy import isprime, primerange
def a(n):
p2 = list(map(str, primerange(10, 100)))
return sum(1 for p in product(p2, repeat=n) if isprime(int("".join(p))))
print([a(n) for n in range(1, 6)]) # Michael S. Branicky, Feb 13 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giorgio Balzarotti & Paolo P. Lava, Dec 07 2007
EXTENSIONS
a(7) from Chai Wah Wu, Nov 29 2015
a(8) from Michael S. Branicky, Feb 12 2023
STATUS
approved