A110068 Numbers n such that 10^(n-1) + pi(n) is the smallest n-digit prime.

2, 6, 23, 78, 5997

Offset

1,1

Comments

In the Cramer model, the chance that there are no primes between 10^(n-1) and 10^(n-1) + pi(n) is 1 + o(1). The same heuristic suggests that there are infinitely many terms since the harmonic series diverges. [Charles R Greathouse IV, Nov 15 2010]

a(6) > 219035. - Robert Price, May 29 2015

Links

Table of n, a(n) for n=1..5.

Prog

(Python)
from sympy import nextprime, primepi
A110068_list = [n for n in range(1, 100) if nextprime(10**(n-1))-10**(n-1) == primepi(n)] # Chai Wah Wu, Apr 29 2018

Crossrefs

Cf. A110065.

Sequence in context: A290954 A220213 A217200 * A247211 A150275 A335537

Adjacent sequences: A110065 A110066 A110067 * A110069 A110070 A110071

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Jul 13 2005

Extensions

a(5) from Charles R Greathouse IV, Nov 15 2010

Status

approved