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

Offset

1,2

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

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.

Mathematica

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

Prog

(PARI) { for (n=1, 200, write("b064536.txt", n, " ", (4^n % 3^n) % 2^n) ) } \\ Harry J. Smith, Sep 17 2009

Crossrefs

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

Sequence in context: A059374 A098384 A243253 * A361456 A324012 A355259

Adjacent sequences: A064533 A064534 A064535 * A064537 A064538 A064539

Keyword

nonn

Author

Labos Elemer, Oct 08 2001

Status

approved