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A057283 Numbers k such that k | 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k. 0

%I #10 Feb 07 2018 02:44:48

%S 1,2,4,10,13,38,50,169,250,1250,2197,2390,3887,5050,6250,18950,25250,

%T 25316,28561,31250,49250,88751,126250,129826,156250,217550,371293,

%U 377750,510050,584233,593750,631250,651157,781250,1106750,1318750,1326250,2550250,3156250,3741491,3906250,4085450,4417550

%N Numbers k such that k | 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k.

%C The only primes in the sequence are 2 and 13. Are all terms except 1 divisible by 2 or 13? - _Robert Israel_, Feb 06 2018

%p select(n -> 10 &^ n + 9 &^ n + 8 &^ n + 7 &^ n + 6 &^ n + 5 &^ n + 4 &^ n + 3 &^ n mod n = 0 , [$1..10^6]); # _Robert Israel_, Feb 06 2018

%t Select[ Range[ 10^6 ], Mod[ PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]

%Y Contains A001022.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000

%E More terms from _Robert Israel_, Feb 06 2018

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Last modified May 13 08:41 EDT 2024. Contains 372498 sequences. (Running on oeis4.)