A232769 - OEIS

%I #31 Jul 19 2016 11:39:39

%S 1,3,111,4107,151959,5622483,22494039,208031871,225121209,832279443,

%T 7697179227,8329484733,27486820443,30794339391,92366302683,

%U 123199851603,230915528769,284795631399,308190935121,1017012356391

%N Numbers n not divisible by 9 such that n divides 10^n - 1 (A014950).

%C The above terms reduced modulo 9 yield: 1, 3, 3, 3, 3, 3, 6, 3, 6, 6, 3, 6, 3, 6, 3, 3, 3, 3, 6, 3, 6, …, .

%C The only primes less than a billion which can divide members of this sequence are 3, 37, 5477, 607837, 1519591, 2028119, 15195911, 18235093, 44988079, 74202397, 247629013, 337349203, 395397319, 462411133, and 674699071. - _Charles R Greathouse IV_, Dec 03 2013

%H Ray Chandler, <a href="/A232769/b232769.txt">Table of n, a(n) for n = 1..55</a>

%t k = 3; lst = {1}; While[k < 10^10 + 1, If[ PowerMod[10, k, k] == 1, AppendTo[ lst, k]; Print@ k]; k += 3; If[ PowerMod[ 10, k, k] == 1, AppendTo[ lst, k]; Print@ k]; k += 6]; lst

%o (PARI) is(n)=n%9 && Mod(10,n)^n==1 \\ _Charles R Greathouse IV_, Dec 03 2013

%o (PARI) forstep(n=1,1e8,[2, 4, 4, 2, 4, 2, 2, 2, 6, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 6, 2, 2, 2, 4, 2, 4, 4, 2, 2], if(Mod(10,n)^n==1,print1(n", "))) \\ _Charles R Greathouse IV_, Dec 03 2013

%Y Cf. A014950.

%K nonn

%O 1,2

%A _Hans Havermann_ and _Robert G. Wilson v_, Nov 29 2013

%E a(22)-a(26) from _Ray Chandler_, Dec 11 2013

%E B-file extended through a(55) by _Ray Chandler_, Dec 24 2013