A104386 Numbers k such that the average of the k-th and (k+1)-th primes is a repdigit.

2, 3, 4, 25, 29, 603, 6363181, 21366409911, 279238341033925, 2907021742443974, 11220808305309952, 11885037375341198280

Offset: 1

Author

Zak Seidov, Mar 04 2005

Keywords

• nonn
• base
• hard
• more

Crossrefs

Cf. A054268.

Corresponding primes A104387, A104388, repdigits A104389.

Programs

Python

from itertools import count, islice
from sympy import isprime, prevprime, primepi
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 primepi(p)
print(list(islice(agen(), 7))) # Michael S. Branicky, Jun 30 2022

Formula

(prime(k) + prime(k+1))/2 = repdigit.

Extensions

a(8) from Giovanni Resta, Apr 05 2006

a(9) from Michael S. Branicky, Jul 02 2022

a(10)-a(12) from Chai Wah Wu, Jun 01 2024