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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. 75
 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 (list; graph; refs; listen; history; text; internal format)
 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: A082522 A279096 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

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Last modified July 9 19:46 EDT 2020. Contains 335545 sequences. (Running on oeis4.)