A114370 Primes p such that the sum of numbers from prime p to nextprime(p)-1 is a repdigit.

2, 3, 5, 53, 55555553, 55555555555555555555555553, 2777777777777777777777777777777777777

Offset

1,1

Comments

The sequence is built under the (reasonable) assumption that 100+2*log(p)^2 is an upper bound to the largest gap between a prime p and nextprime(p). Under this assumption there are no other terms with less than 100 digits.

Links

Table of n, a(n) for n=1..7.

Example

nextprime(55555555555555555555555553) is 55555555555555555555555559 and the sum
from 55555555555555555555555553 to 55555555555555555555555558 gives the repdigit 333333333333333333333333333.

Prog

(Python)
from itertools import count, islice
from sympy import isprime, nextprime
from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A114370_gen(): # generator of terms
    for l in count(1):
        c = []
        for m in range(1, 10):
            k = m*(10**l-1)//9<<1
            for a, b in diop_quadratic((x-y)*(x+y-1)-k):
                if isprime(b) and a == nextprime(b):
                    c.append(b)
        yield from sorted(c)
A114370_list = list(islice(A114370_gen(), 6)) # Chai Wah Wu, Jun 02 2024

Crossrefs

Cf. A010785, A054268.

Sequence in context: A100850 A309607 A060085 * A114725 A136340 A029961

Adjacent sequences: A114367 A114368 A114369 * A114371 A114372 A114373

Keyword

base,nonn,more

Author

Giovanni Resta, Feb 09 2006

Status

approved