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

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Beatty Sequence

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.

Prog

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

Crossrefs

Cf. A066343.

Sequence in context: A059534 A137804 A246414 * A059548 A064720 A029741

Adjacent sequences: A054962 A054963 A054964 * A054966 A054967 A054968

Keyword

base,nonn

Author

Henry Bottomley, Dec 13 2002

Status

approved