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

1,7

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.

Links

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

Example

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

Prog

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

Crossrefs

Cf. A069521 to A069530.

Cf. A000010, A001913, A002329.

Sequence in context: A096693 A193139 A083206 * A335487 A035677 A283470

Adjacent sequences: A069528 A069529 A069530 * A069532 A069533 A069534

Keyword

nonn

Author

Amarnath Murthy, Apr 01 2002

Extensions

More terms from Vladeta Jovovic, Apr 03 2002

Status

approved