A392964 a(n) is the least nonnegative integer such that for all positive integers k, appending zero or more copies of a(n) to k will eventually result in a value divisible by n.

0, 0, 1, 0, 0, 2, 100000, 0, 1, 0, 10, 4, 100000, 100000, 5, 0, 1000000000000000, 2, 100000000000000000, 0, 100000, 10, 1000000000000000000000, 8, 0, 100000, 100, 100000, 1000000000000000000000000000, 10, 100000000000000, 0, 10, 1000000000000000, 100000, 4, 100, 100000000000000000, 100000, 0

Offset

1,6

Comments

The length of a(n) must be a multiple of A051626(d) (or 1, where A051626(d) is zero) for any d dividing n.

Links

Table of n, a(n) for n=1..40.

Hugo van der Sanden, Perl program (GitHub).

Example

a(5)=0 because if we append zero to any positive integer the result will be a multiple of 5.
a(6)=2 because if we append 2 up to three times to any positive integer the result will be a multiple of 6.
a(7)=100000 since A051626(7)=6: for any value less than this there are some k that never give a multiple of 7. For example, appending 1 fails for k=3 since 3, 31, 311, ... are all equivalent to 3 (mod 7). However since 10^6 k + 100000 == k + 5 (mod 7), appending 100000 means that every k will cycle through possible values (mod 7) until reaching a number that is divisible by 7.

Crossrefs

Cf. A051626.

Sequence in context: A060069 A354177 A231612 * A296104 A170995 A319022

Adjacent sequences: A392961 A392962 A392963 * A392965 A392966 A392967

Keyword

nonn,base

Author

Ali Sada and Hugo van der Sanden, Jan 28 2026

Status

approved