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A133900
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a(n) = period of the sequence {b(m), m>=0}, defined by b(m):=binomial(m+n,n) mod n.
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76
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the analogue 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).
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LINKS
| Hieronymus Fischer, Table of n, a(n) for n = 1..111
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FORMULA
| a(n)=n^2 if n is a prime or a power of a prime.
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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).
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CROSSREFS
| Cf. A000040, A001175, A133872-A133880, A133882-A133890, A133910.
Cf. A133620-A133625, A133630, A038509, A133634-A133636.
Cf. A133905.
Sequence in context: A036454 A115648 A082522 * A143480 A050461 A189835
Adjacent sequences: A133897 A133898 A133899 * A133901 A133902 A133903
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 15 2007, Oct 20 2007
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