A153459 Decimal expansion of log_3 (6).

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

Offset: 1

Author

N. J. A. Sloane, Oct 30 2009

Keywords

• nonn
• cons

Comments

Equals the Hausdorff dimension of Pascal's triangle modulo 3 (A083093). In general, the dimension of Pascal's triangle modulo a prime p is log(p*(p+1)/2) / log(p) (see Reiter link, theorem 2 page 117). - Bernard Schott, Dec 01 2022

Examples

			1.6309297535714574370995271143427608542995856401318804278706...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000.
• A. M. Reiter, Determining the dimension of fractals generated by Pascal's triangle, Fibonacci Quarterly, 31(2), 1993, pp. 112-120.
• Wikipedia, List of fractals by Hausdorff dimension (see Pascal triangle modulo 3).
• Index entries for transcendental numbers

Crossrefs

cf. A002391, A016629, A083093, A102525.

Programs

Maple

evalf(log(6)/log(3),80); # Bernard Schott, Dec 01 2022

Mathematica

RealDigits[Log[3, 6], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Formula

Equals A016629 / A002391 = 1 + A102525. - Bernard Schott, Dec 01 2022