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)
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
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