A228113 - OEIS

%I #23 Feb 16 2025 08:33:20

%S 5,21,142,1059,8360,68940,586140,5096885,45085903,404203228,

%T 3663001812,33489858047,308457620524,2858876200536,26639628764285,

%U 249393770865090,2344318815695001,22116397127183516,209317713015989446,1986761935255798075,18906449883376272709

%N First differences of A057793.

%C This sequence is an approximation to the number of primes with n digits (A006879). The error in the approximation is tabulated in A228114.

%C Because A057793(n) = Riemann(10^n) is not defined for n=0, we set its value to zero for our purpose of defining the differences.

%D John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144-146.

%H Vladimir Pletser, <a href="/A228113/b228113.txt">Table of n, a(n) for n = 1..100</a> [a(40)-a(41) corrected by Sean A. Irvine]

%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/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>.

%F a(n) = A057793(n) - A057793(n-1).

%e For n=1, A057793(1) - A057793(0) = 5 - 0 = 5.

%Y Cf. A006879, A057793, A228111, A228112, A228114, A228115, A228116.

%K nonn

%O 1,1

%A _Vladimir Pletser_, Aug 10 2013