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

%I A133900 #8 Jul 11 2015 16:37:17
%S A133900 1,4,9,16,25,72,49,64,81,400,121,864,169,784,675,256,289,2592,361,
%T A133900 1600,1323,3872,529,3456,625,5408,729,3136,841,324000,961,1024,9801,
%U A133900 18496,6125,31104,1369,23104,13689,32000,1681,254016,1849,15488,30375,33856
%N A133900 a(n) = period of the sequence {b(m), m>=0}, defined by b(m):=binomial(m+n,n) mod n.
%C A133900 This is the analog of the sequence of Pisano periods (A001175) for binomial factors.
%C A133900 n^2 always divides a(n).
%C A133900 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).
%H A133900 Hieronymus Fischer, <a href="/A133900/b133900.txt">Table of n, a(n) for n = 1..111</a>
%F A133900 a(n)=n^2 if n is a prime or a power of a prime.
%e A133900 a(3)=9 since binomial(m+3,3) mod 3, m>=0, is periodic with period length 3^2=9 (see A133883).
%e A133900 a(6)=72 since binomial(m+6,6) mod 6, m>=0, is periodic with period length 4*6^2=72 (see A133886).
%Y A133900 Cf. A000040, A001175, A133872-A133880, A133882-A133890, A133910.
%Y A133900 Cf. A133620-A133625, A133630, A038509, A133634-A133636.
%Y A133900 Cf. A133905.
%K A133900 nonn
%O A133900 1,2
%A A133900 _Hieronymus Fischer_, Oct 15 2007, Oct 20 2007