A016579 Decimal expansion of log(5/2).

9, 1, 6, 2, 9, 0, 7, 3, 1, 8, 7, 4, 1, 5, 5, 0, 6, 5, 1, 8, 3, 5, 2, 7, 2, 1, 1, 7, 6, 8, 0, 1, 1, 0, 7, 1, 4, 5, 0, 1, 0, 1, 2, 1, 9, 9, 0, 8, 2, 6, 2, 4, 6, 7, 7, 9, 1, 9, 6, 7, 8, 8, 1, 9, 8, 0, 7, 8, 5, 3, 6, 5, 7, 3, 7, 9, 6, 3, 0, 4, 9, 0, 2, 4, 2, 7, 0, 5, 5, 1, 0, 9, 6, 7, 6, 0, 9, 2

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			0.916290731874155065183527211768011071450101219908262467791967881980785...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Index entries for transcendental numbers

Crossrefs

Cf. A016530 (continued fraction).

Programs

Magma

SetDefaultRealField(RealField(100)); Log(5/2); // Vincenzo Librandi, Apr 07 2020

Mathematica

RealDigits[Log[5/2], 10, 120][[1]] (* Vincenzo Librandi, Apr 07 2020 *)

PARI

default(realprecision, 20080); x=10*log(5/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b016579.txt", n, " ", d)); \\ Harry J. Smith, May 25 2009

Formula

Equals A016628 minus A002162. - R. J. Mathar, Jan 23 2009

log(5/2) = 2*Sum_{n >= 1} 1/(n*P(n, 7/3)*P(n-1, 7/3)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(5/2) = 0.916290731874155065183527(19...), correct to 24 decimal places. - Peter Bala, Mar 18 2024

Extensions

Leading zero removed and offset adjusted by R. J. Mathar, Feb 06 2009