A135945 Number of primes with 2n digits made of adjacent primes with 2 digits.

21, 80, 1972, 26108, 473297, 7854396, 144622191, 2620370968

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).

Links

Table of n, a(n) for n=1..8.

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

Cf. A135944, A135946.

Sequence in context: A172082 A296970 A068085 * A158493 A159743 A219593

Adjacent sequences: A135942 A135943 A135944 * A135946 A135947 A135948

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