A054965 Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 132, 134, 136

Offset: 1

Author

Henry Bottomley, Dec 13 2002

Keywords

• base
• nonn

Examples

			log_10(3) = 0.477121... so a(11) = floor(11/0.477121...) = floor(23.0549...) = 23; 3^23 = 94143178827 is the largest 11 decimal digit power of 3.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences.

Crossrefs

Cf. A062153, A066343, A074118, A152566.

Programs

Mathematica

Floor[Range[100]*Log[3, 10]] (* Paolo Xausa, Jul 11 2024 *)

PARI

a(n) = n*log(10)\log(3); \\ Michel Marcus, Aug 03 2017

Formula

a(n) = floor(n/log_10(3)) = log_3(A074118(n)) = A062153(A074118(n)).