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

Author

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

Keywords

• nonn
• base
• easy

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.

Crossrefs

Cf. A000030, A000244.

Programs

Mathematica

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

PARI

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

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

Extensions

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