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%I #22 May 15 2019 11:36:12
%S 1,1,0,5,5,5,0,4,2,7,5,2,0,9,0,8,9,3,7,0,9,6,0,9,0,1,3,9,9,5,3,9,2,5,
%T 6,5,9,7,0,0,4,9,6,9,4,6,9,1,1,6,3,6,2,8,9,3,1,4,6,0,0,3,4,3,7,2,0,6,
%U 3,4,1,7,1,4,0,3,2,5,9,8,2,1,7,3,9,8,1,1,9,1,0,4,6,9,5,7,3,9,3,9,1,4,7,1,8
%N Decimal expansion of log(6^9*10^5)/25.
%C The value is equal to 6/5*(log(2)/2 + log(3)/3 + log(5)/5 - log(30)/30) = (6/5)*A230191.
%C Pafnuty Chebyshev proved in 1852 that A*x/log(x) < pi(x) < B*x/log(x) holds for all x >= x(0) with some x(0) sufficiently large, where A = 5/6*B and B is the constant given above.
%D Harold M. Edwards, Riemann's zeta function, Dover Publications, Inc., New York, 2001, pp. 281-284.
%H P. L. Chebyshev, <a href="http://sites.mathdoc.fr/JMPA/PDF/JMPA_1852_1_17_A19_0.pdf">Mémoire sur les nombres premiers</a>, Journal de Math. Pures et Appl. 17 (1852), 366-390.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">Prime number theorem</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 1.105550427520908937096090139953925659700496946911636289314600343720634...
%t RealDigits[Log[6^9 10^5]/25,10,120][[1]] (* _Harvey P. Dale_, Mar 14 2015 *)
%o (PARI) default(realprecision, 105); x=log(6^9*10^5)/25; for(n=1, 105, d=floor(x); x=(x-d)*10; print1(d, ", "));
%Y Cf. A000040, A000720, A230191.
%K nonn,cons
%O 1,4
%A _Arkadiusz Wesolowski_, Oct 11 2013