A141492 a(n) is the floor of the reciprocal of the difference between the 10^n-th root of 10^n and 1.

3, 21, 144, 1085, 8685, 72381, 620420, 5428680, 48254941, 434294481, 3948131653, 36191206824, 334072678386, 3102103442165, 28952965460216, 271434051189531, 2554673422960304, 24127471216847323, 228576043106974645, 2171472409516259137, 20680689614440563220

Offset

1,1

Comments

Conjecture: This sequence converges to the number of primes < 10^n or Pi(10^n).

From Jon E. Schoenfield, Aug 05 2021: (Start)

Define f(x) = 1/(x^(1/x) - 1). As x increases, f(x) -> 1/y - 1/2 + y/12 - y^3/720 + y^5/30240 + ... where y = log(x)/x. So if we let x = 10^n, then we have (see Formula section) a(n) = floor(f(10^n)) and, as n increases, f(10^n) = 1/((10^n)^(1/10^n) - 1) -> 10^n/(log(10)*n) - 1/2 + (log(10)/12)*n/10^n - ...

Conjecture: a(n) = floor(10^n/(log(10)*n) - 1/2) for n >= 1. (End)

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = floor(1/((10^n)^(1/10^n) - 1)).

Prog

(PARI) for(x=1, n, y=1/((10^x)^(1/10^x)-1); print1(floor(y)", "))

Crossrefs

Cf. A006880.

Sequence in context: A228115 A377096 A033888 * A243397 A173350 A323203

Adjacent sequences: A141489 A141490 A141491 * A141493 A141494 A141495

Keyword

nonn

Author

Cino Hilliard, Aug 10 2008

Extensions

Name corrected and a(20)-a(21) from Jon E. Schoenfield, Aug 05 2021

Status

approved