A054869 - OEIS

%I #34 Dec 05 2022 21:40:33

%S 3,1,2,0,5,3,1,2,2,2,5,1,5,5,1,4,1,3,1,2,5,5,5,0,5,2,5,5,5,3,1,4,3,3,

%T 0,4,2,2,4,0,1,3,3,1,4,0,2,0,1,2,5,2,4,0,2,3,3,0,3,4,5,5,2,5,5,4,3,2,

%U 3,1,5,4,5,4,0,1,1,0,4,2,0,1,3,0,1,5,0,4,3,5,0,1,0,2,4,0,3,4,2

%N Digits of an idempotent 6-adic number.

%C ( a(0) + a(1)*6 + a(2)*6^2 + ... )^k = a(0) + a(1)*6 + a(2)*6^2 + ... for each k. Apart from 0 and 1, in base 6 there are only 2 numbers with this property. For the other see A055620.

%D V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.

%H Kenny Lau, <a href="/A054869/b054869.txt">Table of n, a(n) for n = 0..9999</a>

%H V. deGuerre and R. A. Fairbairn, <a href="/A003226/a003226.pdf">Automorphic numbers</a>, Jnl. Rec. Math., 1 (No. 3, 1968), 173-179

%F a(n) == 3^(2^n) (mod 6^n). - _Robert Dawson_, Oct 28 2022

%o (Python)

%o n=10000;res=1-pow((3**n+1)//2,n,3**n)*2**n

%o for i in range(n):print(i,res%6);res//=6

%o # _Kenny Lau_, Jun 09 2018

%Y The six examples given by deGuerre and Fairbairn are A055620, A054869, A018247, A018248, A259468, A259469.

%K nonn,base

%O 0,1

%A Paolo Dominici (pl.dm(AT)libero.it), May 23 2000