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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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78
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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FORMULA
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a(n)=n^2 if n is a prime or a power of a prime.
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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