A135946 Number of primes with 3n digits made of adjacent primes with 3 digits.

143, 2753, 415639, 36573197, 4566059881

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).

Links

Table of n, a(n) for n=1..5.

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

Cf. A135944, A135945.

Sequence in context: A185514 A220292 A159054 * A217534 A279115 A199039

Adjacent sequences: A135943 A135944 A135945 * A135947 A135948 A135949

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