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Difference of consecutive integers nearest to Li(10^n) - Li(2), where Li(x) = integral(0..x, dt/log(t)) (A190802, known as Gauss' approximation for the number of primes below 10^n).
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%I #17 Feb 16 2025 08:33:20

%S 5,24,148,1068,8384,68998,586290,5097291,45087026,404206380,

%T 3663010786,33489883880,308457695529,2858876419882,26639629409596,

%U 249393772773269,2344318821362265,22116397144079593,209317713066531967,1986761935407441102

%N Difference of consecutive integers nearest to Li(10^n) - Li(2), where Li(x) = integral(0..x, dt/log(t)) (A190802, known as Gauss' approximation for the number of primes below 10^n).

%C This sequence gives a good approximation of the number of primes with n digits (A006879); see (A228068).

%C Note that A190802(n)=(Li(10^n)-Li(2)) is not defined for n=0. Its value is arbitrarily set to 0.

%H Vladimir Pletser, <a href="/A228067/b228067.txt">Table of n, a(n) for n = 1..500</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>

%F a(n) = A190802(n) - A190802(n-1).

%e For n = 1, A190802(1) - A190802(0) = 5-0 = 5.

%Y Cf. A006879, A190802, A228068, A228065.

%K nonn,changed

%O 1,1

%A _Vladimir Pletser_, Aug 06 2013