A230192 - OEIS

A230192

Decimal expansion of log(6^9*10^5)/25.

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, 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, 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

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OFFSET

1,4

COMMENTS

The value is equal to 6/5*(log(2)/2 + log(3)/3 + log(5)/5 - log(30)/30) = (6/5)*A230191.

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.

REFERENCES

Harold M. Edwards, Riemann's zeta function, Dover Publications, Inc., New York, 2001, pp. 281-284.

LINKS

Table of n, a(n) for n=1..105.

P. L. Chebyshev, Mémoire sur les nombres premiers, Journal de Math. Pures et Appl. 17 (1852), 366-390.

Wikipedia, Prime number theorem

Index entries for transcendental numbers

EXAMPLE

1.105550427520908937096090139953925659700496946911636289314600343720634...

MATHEMATICA

RealDigits[Log[6^9 10^5]/25, 10, 120][[1]] (* Harvey P. Dale, Mar 14 2015 *)

PROG