A064536 - OEIS

%I #14 Dec 30 2024 12:51:44

%S 1,3,2,13,20,3,51,87,121,711,1139,3537,8034,15752,27922,49629,33201,

%T 35975,143900,136341,545364,2181456,1060135,4240540,16962160,28647197,

%U 13597858,205877827,100616667,381266393,1397863922,3825576990,8216376565,14181633879,22366797148

%N a(n) = (4^n mod 3^n) mod 2^n.

%C A generalization of A002380. It arises also as a coefficient (=c1) of 1^n=1 in a special (greedy) decomposition of 4^n into like powers as follows: 4^n = c3*3^n + c2*2^n + c1*1^n.

%H Harry J. Smith, <a href="/A064536/b064536.txt">Table of n, a(n) for n = 1..200</a>

%F n = 7: 4^7 = 16384 = 7*2187 + 8*128 + 51*1 where a(7)=51, the last coefficient; A064630(7) = 7 + 8 + a(7) = 66.

%t Table[Mod[PowerMod[4,n,3^n],2^n],{n,40}] (* _Harvey P. Dale_, Apr 09 2013 *)

%o (PARI) a(n) = { (4^n % 3^n) % 2^n } \\ _Harry J. Smith_, Sep 17 2009

%Y Cf. A002380, A064853-A064855, A060692, A064628-A064631.

%K nonn

%O 1,2

%A _Labos Elemer_, Oct 08 2001