cp's OEIS Frontend

A057292 Numbers k such that k | 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k + 1^k.

%I A057292 #14 Jun 25 2025 19:20:43
%S A057292 1,2,3,9,11,22,27,33,46,81,99,121,209,242,243,297,363,729,891,1058,
%T A057292 1089,1179,1331,1702,2187,2662,2673,3082,3267,3993,6561,8019,9801,
%U A057292 11979,14641,19683,20673,24057,24334,25029,29282,29403,30591,30734
%N A057292 Numbers k such that k | 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k + 2^k + 1^k.
%C A057292 The only primes in the sequence are 2, 3 and 11. - _Robert Israel_, Jun 25 2025
%H A057292 Robert Israel, <a href="/A057292/b057292.txt">Table of n, a(n) for n = 1..227</a>
%p A057292 filter:= n ->  11&^n + 10&^n + 9&^n + 8&^n + 7&^n + 6&^n + 5&^n + 4&^n + 3&^n + 2&^n + 1 mod n = 0:
%p A057292 select(filter, [$1..10^5]); # _Robert Israel_, Jun 25 2025
%t A057292 Select[ Range[ 10^5 ], Mod[ PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ] + 1, # ] == 0 & ]
%t A057292 Select[Range[31000],Mod[Total[PowerMod[Range[0,11],#,#]],#]==0&] (* _Harvey P. Dale_, Nov 22 2021 *)
%Y A057292 Cf. A056739, A057291, A103438.
%K A057292 nonn
%O A057292 1,2
%A A057292 _Robert G. Wilson v_, Sep 22 2000