A057493 Numbers n such that n | 11^n + 10^n.

1, 3, 7, 9, 21, 27, 49, 63, 81, 111, 147, 171, 189, 203, 243, 333, 343, 441, 513, 567, 609, 729, 777, 999, 1029, 1143, 1197, 1323, 1421, 1539, 1701, 1791, 1827, 2187, 2331, 2401, 2943, 2997, 3087, 3249, 3429, 3591, 3969, 4107, 4263, 4617, 5103, 5373

Offset: 1

Author

Robert G. Wilson v, Sep 20 2000

Keywords

• nonn

Comments

From Robert Israel, Feb 23 2017: (Start)

Contains A003594.

Every term other than 1 is divisible by 3 or 7.

If m and n are in the sequence, then so is m*n. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..5305 (first 580 terms from Vincenzo Librandi)

Crossrefs

Cf. A003594.

Programs

Maple

select(t -> (10 &^ t + 11 &^ t mod t = 0), [seq(i,i=1..10000,2)]); # Robert Israel, Feb 23 2017

Mathematica

Select[ Range[ 10000 ], Mod[ PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ], # ] == 0 & ]

PARI

is(n)=Mod(11,n)^n+Mod(10,n)^n==0 \\ Charles R Greathouse IV, Feb 23 2017