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

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• nonn

Comments

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.

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A069521 to A069530.

Cf. A000010, A001913, A002329.

Programs

PARI

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

Extensions

More terms from Vladeta Jovovic, Apr 03 2002