A160590 Next-to-least significant digit of 2^n.

1, 3, 6, 2, 5, 1, 2, 4, 9, 9, 8, 6, 3, 7, 4, 8, 7, 5, 0, 0, 1, 3, 6, 2, 5, 1, 2, 4, 9, 9, 8, 6, 3, 7, 4, 8, 7, 5, 0, 0, 1, 3, 6, 2, 5, 1, 2, 4, 9, 9, 8, 6, 3, 7, 4, 8, 7, 5, 0, 0, 1, 3, 6, 2, 5, 1, 2, 4, 9, 9, 8, 6, 3, 7, 4, 8, 7, 5, 0, 0, 1, 3, 6, 2, 5, 1, 2, 4, 9, 9, 8, 6, 3, 7, 4, 8, 7, 5, 0, 0, 1, 3, 6, 2, 5

Offset: 4

Author

Brian Tristam Williams (briantw(AT)briantw.com), May 20 2009

Keywords

• nonn
• base
• easy

Comments

In the sequence [1, 2, 4, 8,] 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, (A000079) the least-significant digit recurs as [..], 6,2,4,8.. (A000689).

The second-least-significant digit repeats in the sequence [..],1,3,6,2,5,1,2,4,9,9,8,6,3,7,4,8,7,5,0,0...

Links

• Paolo Xausa, Table of n, a(n) for n = 4..10000
• M. Haapanen, What is this and how to prove?, newgsroups sci.math, Mar 28 1996
• K. Makella, Mika luku tulee seuraavana?, sfnet.tiede.matematiikka, Jan 2008
• Lars Radvall, Multiplar (PDF).
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A000079, A000689.

Programs

Maple

for n from 4 to 130 do 2 &^ n mod 100 ; printf("%d,", floor(%/10)) ; od:

Mathematica

PadRight[{},100,{1,3,6,2,5,1,2,4,9,9,8,6,3,7,4,8,7,5,0,0}] (* Paolo Xausa, Oct 22 2023 *)

Formula

Periodic: a(n+20) = a(n).

Extensions

Edited by R. J. Mathar, May 22 2009