A104389 Repdigits which are the average of two successive primes.

4, 6, 9, 99, 111, 4444, 111111111, 555555555555, 9999999999999999, 111111111111111111, 444444444444444444, 555555555555555555555, 777777777777777777777777, 333333333333333333333333333333333, 444444444444444444444444444444444444

Offset: 1

Author

Zak Seidov, Mar 04 2005

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..31

Crossrefs

Corresponding primes: A104387, A104388.

Cf. A054268, A104386, A104387, A104388.

Programs

Python

from itertools import count, islice
from sympy import isprime, prevprime
def agen():
    for d in count(1):
        ru = int("1"*d)
        for r in range(ru, 10*ru, ru):
            if r > 2:
                p = prevprime(r)
                if isprime(r + (r-p)) and prevprime(r+(r-p)) == p:
                    yield r
print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 30 2022

Formula

a(n) = (A104387(n)+A104388(n))/2.

Extensions

More terms from Giovanni Resta, Apr 05 2006