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

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.

Sequence in context: A008564 A348371 A354129 * A125301 A347214 A263559

Adjacent sequences: A060953 A060954 A060955 * A060957 A060958 A060959

Keyword

nonn,base,easy

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 08 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

Status

approved