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

1, 3, 9, 27, 81, 99, 243, 249, 729, 2187, 2781, 6561, 8019, 8667, 19683, 36207, 59049, 110457, 131549, 161269, 177147, 531441, 649539, 990711, 1325787, 1594323, 1633689, 4782969

Offset

1,2

Comments

From Robert Israel, Jan 02 2019: (Start)

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

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)

Links

Robert Israel, Table of n, a(n) for n = 1..53

Maple

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

Mathematica

Select[ Range[ 10^6 ], Mod[ PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ], # ] == 0 & ]
Select[Range[5*10^6], Divisible[Total[PowerMod[{10, 9, 8}, #, #]], #]&] (* Harvey P. Dale, Feb 04 2015 *)

Crossrefs

Contains A000244.

Sequence in context: A036136 A271350 A057262 * A036145 A014950 A271351

Adjacent sequences: A057229 A057230 A057231 * A057233 A057234 A057235

Keyword

nonn

Author

Robert G. Wilson v, Sep 20 2000

Extensions

More terms from Harvey P. Dale, Feb 04 2015

Status

approved