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%I #29 Feb 07 2024 20:39:24
%S 5,29,177,1245,9629,78627,664917,5762208,50849234,455055614,
%T 4118066400,37607950280,346065645809,3204942065691,29844571475287,
%U 279238344248556,2623557165610821,24739954309690414,234057667376222381,2220819602783663483
%N Gauss' approximation for the number of primes below 10^n.
%C 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
%D Jonathan Borwein, David H. Bailey, "Mathematics by Experiment", A. K. Peters, 2004, p. 65 (Table 2.2).
%H Vladimir Pletser, <a href="/A190802/b190802.txt">Table of n, a(n) for n = 1..500</a>
%H Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, <a href="https://arxiv.org/abs/1807.08899">The Bateman-Horn Conjecture: Heuristics, History, and Applications</a>, arXiv:1807.08899 [math.NT], 2018-2019. See Table 1 p. 6.
%F a(n) = round(integral(dt/log(t),t=2..10^n)).
%p seq(round(evalf(integrate(1/log(t),t=2..10^n))), n=1..21);
%t Table[Round[Integrate[1/Log[t],{t,2,10^n}]],{n,20}] (* _James C. McMahon_, Feb 06 2024 *)
%Y Cf. A006880, A106313.
%K nonn
%O 1,1
%A _Nathaniel Johnston_, May 25 2011
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