A064855 a(n) = (((6^n mod 5^n) mod 4^n) mod 3^n) mod 2^n.

1, 2, 0, 14, 16, 10, 66, 21, 321, 917, 2037, 1550, 2420, 15152, 27439, 46731, 110953, 137148, 336949, 703202, 805647, 181132, 5835407, 3343039, 21816283, 18528238, 95129681, 241918238, 311938330, 48698222, 1539688558, 3481498150, 8104918325, 13512884439, 22365723609

Offset: 1

Author

Labos Elemer, Oct 08 2001

Keywords

• nonn

Comments

A generalization of A002380, A064536 and A064854. It arises also as a coefficient (=c1) of 1^n=1 in a special (greedy) decomposition of 6^n into like powers as follows: 6^n = c5*5^n + c4*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, A064536, A064854, A064855, A060692, A064628-A064631.

Programs

Mathematica

Table[Fold[Mod,6^n,Range[5,2,-1]^n],{n,40}]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

a(n) = { (((6^n%5^n)%4^n)%3^n)%2^n } \\ Harry J. Smith, Sep 28 2009

Formula

n = 8: 6^8 = 1679616 = 4*390625 + 1*65536 + 7*6561 + 22*256 + 21*1 where a(8)=21, the last coefficient and here 6^8 is decomposed into 4 + 1 + 7 + 22 + 21 = 55 like (8th) powers.