A133900 a(n) = period of the sequence {b(m), m>=0}, defined by b(m):=binomial(m+n,n) mod n.

1, 4, 9, 16, 25, 72, 49, 64, 81, 400, 121, 864, 169, 784, 675, 256, 289, 2592, 361, 1600, 1323, 3872, 529, 3456, 625, 5408, 729, 3136, 841, 324000, 961, 1024, 9801, 18496, 6125, 31104, 1369, 23104, 13689, 32000, 1681, 254016, 1849, 15488, 30375, 33856

Offset

1,2

Comments

This is the analog of the sequence of Pisano periods (A001175) for binomial factors.

n^2 always divides a(n).

A prime p is a factor of a(n) if and only if it is a factor of n (i.e., a(n) and n have the same prime factors).

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..111

Formula

a(n)=n^2 if n is a prime or a power of a prime.

Example

a(3)=9 since binomial(m+3,3) mod 3, m>=0, is periodic with period length 3^2=9 (see A133883).
a(6)=72 since binomial(m+6,6) mod 6, m>=0, is periodic with period length 4*6^2=72 (see A133886).

Crossrefs

Cf. A000040, A001175, A133872-A133880, A133882-A133890, A133910.

Cf. A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133905.

Sequence in context: A279096 A374927 A299153 * A143480 A230365 A274963

Adjacent sequences: A133897 A133898 A133899 * A133901 A133902 A133903

Keyword

nonn

Author

Hieronymus Fischer, Oct 15 2007, Oct 20 2007

Status

approved