A056968 10^(n-1) modulo n.

0, 0, 1, 0, 0, 4, 1, 0, 1, 0, 1, 4, 1, 10, 10, 0, 1, 10, 1, 0, 16, 10, 1, 16, 0, 10, 19, 20, 1, 10, 1, 0, 1, 10, 25, 28, 1, 10, 22, 0, 1, 40, 1, 32, 10, 10, 1, 16, 8, 0, 49, 12, 1, 46, 45, 24, 43, 10, 1, 40, 1, 10, 37, 0, 55, 10, 1, 48, 31, 20, 1, 64, 1, 10, 25, 12, 67, 4, 1, 0, 73, 10, 1

Offset: 1

Author

Henry Bottomley, Jul 20 2000

Keywords

• nonn
• look

Examples

			a(6)=4 since 100000=6*16666+4
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003592, A053041, A056969.

Programs

Maple

0, seq(10&^(n-1) mod n, n=2..100); # Robert Israel, Nov 25 2024

Mathematica

Table[PowerMod[10,n-1,n],{n,100}] (* Harvey P. Dale, Jul 17 2021 *)

Formula

If n is of form 2^i*5^j then a(n)=0, otherwise a(n)=10^(n-1)+n-A053041(n)

From Robert Israel, Nov 25 2024: (Start)

If n is prime other than 2 or 5, then a(n) = 1.

If n = 2^i * 5^j * p where p is a prime > 10^(2^i * 5^j), then a(n) = 10^(2^i * 5^j).

If n = 2^i * 5^j * p where p is a prime and

2^(2^i * 5^j - 1 - i) * 5^(2^i * 5^j -1 - j) > p > 2^(2^i * 5^j-2 - u) * 5^(2^i * 5^j-1-j),

then a(n) = 10^(2^i * 5^j - 1) - 2^i * 5^j * p.

For example, with i = 0 and j = 1 we get a(5*p) = 10^4 - 5*p if p is a prime between 1000 and 2000.

(End)