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

1,6

Links

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

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)

Example

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

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 *)

Crossrefs

Cf. A003592, A053041, A056969.

Sequence in context: A161739 A291574 A094924 * A340221 A213541 A181435

Adjacent sequences: A056965 A056966 A056967 * A056969 A056970 A056971

Keyword

nonn,look

Author

Henry Bottomley, Jul 20 2000

Status

approved