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A069531 Smallest positive k such that 10^k + 1 is divisible by n, or 0 if no such number exists. 2

%I

%S 1,0,0,0,0,0,3,0,0,0,1,0,3,0,0,0,8,0,9,0,0,0,11,0,0,0,0,0,14,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,23,0,21,0,0,0,0,0,0,0,0,0,29,0,30,0,0,0,0,

%U 0,0,0,0,0,0,0,4,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,22,0,3,0,0,0,0,0,48,0,0,0,2

%N Smallest positive k such that 10^k + 1 is divisible by n, or 0 if no such number exists.

%C When a(n) is not zero, it is a divisor of phi(n). If n is a prime with primitive root 10 (cf. A001913) then a(n) = (n-1)/2.

%H Antti Karttunen, <a href="/A069531/b069531.txt">Table of n, a(n) for n = 1..10001</a>

%e a(7) = a(13) = 3 as 1001 is divisible by 7 and 13. a(17) = 8 as 17 divides 100000001 = 10^8 + 1.

%o (PARI) A069531(n) = { fordiv(eulerphi(n),k,if(!((1+(10^k))%n),return(k))); (0); }; \\ _Antti Karttunen_, Aug 23 2019

%Y Cf. A069521 to A069530.

%Y Cf. A000010, A001913, A002329.

%K nonn

%O 1,7

%A _Amarnath Murthy_, Apr 01 2002

%E More terms from _Vladeta Jovovic_, Apr 03 2002

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Last modified October 14 12:21 EDT 2019. Contains 328006 sequences. (Running on oeis4.)