A133905 -id:A133905 - cp's OEIS frontend

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

Hieronymus Fischer, Oct 15 2007, Oct 20 2007

nonn

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).

			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).

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

Cf. A000040, A001175, A133872-A133880, A133882-A133890, A133910.
Cf. A133620-A133625, A133630, A038509, A133634-A133636.
Cf. A133905.

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

cp's OEIS Frontend

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

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