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A057232 Numbers n such that n | 10^n + 9^n + 8^n. 1

%I

%S 1,3,9,27,81,99,243,249,729,2187,2781,6561,8019,8667,19683,36207,

%T 59049,110457,131549,161269,177147,531441,649539,990711,1325787,

%U 1594323,1633689,4782969

%N Numbers n such that n | 10^n + 9^n + 8^n.

%C From _Robert Israel_, Jan 02 2019: (Start)

%C All terms are odd, and none are divisible by 5, 7 or 13.

%C If p is a prime > 3 that divides 8^(3^k)+9^(3^k)+10^(3^k), then 3^k*p is in the sequence. (End)

%H Robert Israel, <a href="/A057232/b057232.txt">Table of n, a(n) for n = 1..53</a>

%p select(t -> 8&^t + 9&^t + 10&^t mod t = 0, [seq(seq(10*i+j),j=[1,3,7,9]),i=0..10^6)]); # _Robert Israel_, Jan 02 2019

%t Select[ Range[ 10^6 ], Mod[ PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ], # ] == 0 & ]

%t Select[Range[5*10^6],Divisible[Total[PowerMod[{10,9,8},#,#]],#]&] (* _Harvey P. Dale_, Feb 04 2015 *)

%Y Contains A000244.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 20 2000

%E More terms from _Harvey P. Dale_, Feb 04 2015

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)