A057293 Numbers k such that k | 12^k + 11^k + 1.

1, 2, 3, 9, 14, 15, 27, 38, 51, 81, 98, 135, 243, 266, 658, 686, 722, 729, 1215, 1431, 1862, 2187, 2506, 4131, 4802, 5054, 6561, 8469, 9027, 10755, 10935, 13034, 13718, 19683, 25574, 26602, 33614, 35378, 36315, 45009, 46018, 59049, 82377, 91238

Offset

1,2

Comments

From Robert Israel, Feb 06 2018: (Start)

The only primes in the sequence are 2 and 3.

No terms are divisible by 4.

All terms divisible by 3 are odd.

(End)

This sequence is infinite because 3^j is a term. - Jinyuan Wang, Mar 02 2019

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..224 (first 125 terms from Robert Israel)

Maple

select(n -> 12 &^ n + 11 &^ n + 1 mod n = 0, [$1..10^6]); # Robert Israel, Feb 06 2018

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + 1, # ] == 0 & ]

Crossrefs

Contains A000244.

Sequence in context: A269154 A358829 A225792 * A109662 A116222 A338234

Adjacent sequences: A057290 A057291 A057292 * A057294 A057295 A057296

Keyword

nonn

Author

Robert G. Wilson v, Sep 22 2000

Status

approved