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

1,1

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.

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A062153, A066343, A074118, A152566.

Sequence in context: A059534 A137804 A246414 * A059548 A064720 A376952

Adjacent sequences: A054962 A054963 A054964 * A054966 A054967 A054968

Keyword

base,nonn,changed

Author

Henry Bottomley, Dec 13 2002

Status

approved