A064536 a(n) = (4^n mod 3^n) mod 2^n.

1, 3, 2, 13, 20, 3, 51, 87, 121, 711, 1139, 3537, 8034, 15752, 27922, 49629, 33201, 35975, 143900, 136341, 545364, 2181456, 1060135, 4240540, 16962160, 28647197, 13597858, 205877827, 100616667, 381266393, 1397863922, 3825576990, 8216376565, 14181633879, 22366797148

Offset: 1

Author

Labos Elemer, Oct 08 2001

Keywords

• nonn

Comments

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.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200

Crossrefs

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

Programs

Mathematica

Table[Mod[PowerMod[4,n,3^n],2^n],{n,40}] (* Harvey P. Dale, Apr 09 2013 *)

PARI

a(n) = { (4^n % 3^n) % 2^n } \\ Harry J. Smith, Sep 17 2009

Formula

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.