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

Author

Giovanni Resta, Feb 09 2006

Keywords

• base
• nonn
• more

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.

Examples

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

Crossrefs

Cf. A010785, A054268.

Programs

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