A104387 Larger of two successive primes the average of which is a repdigit.

5, 7, 11, 101, 113, 4447, 111111113, 555555555559, 10000000000000061, 111111111111111131, 444444444444444469, 555555555555555555619, 777777777777777777777787, 333333333333333333333333333333373, 444444444444444444444444444444444497

Offset

1,1

Comments

Lesser primes A104388, repdigits A104389. What is the next term?

The next term is 444444444444444444444444444444444497. The first term with more than 100 digits is a(22) which has 109 digits. - Harvey P. Dale, Jun 28 2011

Links

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

Formula

a(n) = prime(A104386(n)+1).

Mathematica

Union[Flatten[Table[NextPrime/@Select[FromDigits/@Table[PadLeft[{i}, n, i], {n, 45}], Mean[{NextPrime[#], NextPrime[#, -1]}]==#&], {i, 9}]]] (* Harvey P. Dale, Jun 28 2011 *)

Prog

(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 2*r - p
print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 30 2022

Crossrefs

Cf. A054268, A104386, A104388, A104389.

Sequence in context: A027728 A218275 A086140 * A133761 A057659 A098040

Adjacent sequences: A104384 A104385 A104386 * A104388 A104389 A104390

Keyword

nonn,base

Author

Zak Seidov, Mar 04 2005

Extensions

More terms from Giovanni Resta, Apr 05 2006

Status

approved