OFFSET
1,1
COMMENTS
The offset logarithmic integral or Eulerian logarithmic integral Li(10^n)-Li(2), i.e., integral(2..x, dt/log(t)), appears in Gauss’s formula for counting prime numbers < 10^n and is sometimes referred to as the "European" definition. - Vladimir Pletser, Mar 17 2013
REFERENCES
Jonathan Borwein, David H. Bailey, "Mathematics by Experiment", A. K. Peters, 2004, p. 65 (Table 2.2).
LINKS
Vladimir Pletser, Table of n, a(n) for n = 1..500
Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, The Bateman-Horn Conjecture: Heuristics, History, and Applications, arXiv:1807.08899 [math.NT], 2018-2019. See Table 1 p. 6.
FORMULA
a(n) = round(integral(dt/log(t),t=2..10^n)).
MAPLE
seq(round(evalf(integrate(1/log(t), t=2..10^n))), n=1..21);
MATHEMATICA
Table[Round[Integrate[1/Log[t], {t, 2, 10^n}]], {n, 20}] (* James C. McMahon, Feb 06 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, May 25 2011
STATUS
approved