A230191 Decimal expansion of log( 2^(1/2)*3^(1/3)*5^(1/5) / 30^(1/30) ).
9, 2, 1, 2, 9, 2, 0, 2, 2, 9, 3, 4, 0, 9, 0, 7, 8, 0, 9, 1, 3, 4, 0, 8, 4, 4, 9, 9, 6, 1, 6, 0, 4, 7, 1, 6, 4, 1, 7, 0, 8, 0, 7, 8, 9, 0, 9, 3, 0, 3, 0, 2, 4, 1, 0, 9, 5, 5, 0, 0, 2, 8, 6, 4, 3, 3, 8, 6, 1, 8, 0, 9, 5, 0, 2, 7, 1, 6, 5, 1, 8, 1, 1, 6, 5, 0, 9, 9, 2, 5, 3, 9, 1, 3, 1, 1, 6, 1, 5, 9, 5, 5, 9, 8, 6
Offset: 0
Examples
0.921292022934090780913408449961604716417080789093030241095500286433861...
References
- Harold M. Edwards, Riemann's zeta function, Dover Publications, Inc., New York, 2001, pp. 281-284.
- Kolmogorov, A.N., Yushkevich, A.P. (Eds.), Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, Birkhaeser-Verlag, 1992. See p. 185. - N. J. A. Sloane, Jan 20 2019
- Sadegh Nazardonyavi, Improved explicit bounds for some functions of prime numbers, Functiones et Approximatio Commentarii Mathematici 58:1 (2018), pp. 7-22.
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 164.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
- Pafnuty Lvovich 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.
Programs
-
Mathematica
First[RealDigits[Log[6^9*10^5]/30, 10, 100]] (* Paolo Xausa, Apr 01 2024 *)
-
PARI
default(realprecision, 105); x=log(6^9*10^5)/3; for(n=1, 105, d=floor(x); x=(x-d)*10; print1(d, ", "));
Formula
Equals log(6^9*10^5)/30.
Equals log(2)/2 + log(3)/3 + log(5)/5 - log(30)/30 = (5/6)*A230192.
Extensions
Better definition from N. J. A. Sloane, Jan 20 2019
Comments