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A060956

Leading digit of 3^n.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

He, Xinwei; Hildebrand, A J; Li, Yuchen; Zhang, Yunyi, Complexity of Leading Digit Sequences, Discrete Mathematics and Theoretical Computer Science; 22 (2020), #14.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Dmitry Kamenetsky, First digit of 3^2020, Puzzling StackExchange.

FORMULA

a(n) = floor(3^n / 10^floor(log_10(3^n))) = floor( 3^n / 10^floor(n*log_10(3)) ).

a(n) = A000030(A000244(n)). - Michel Marcus, Jul 03 2018

MATHEMATICA

First[IntegerDigits[#]]&/@(3^Range[0, 110]) (* Harvey P. Dale, May 16 2016 *)

PROG

(PARI) a(n) = { 3^n \ 10^logint(3^n, 10) } \\ Harry J. Smith, Jul 15 2009

CROSSREFS

Cf. A000030, A000244.