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A086892
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Greatest common divisor of 2^n-1 and 3^n-1.
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7
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1, 1, 1, 5, 1, 7, 1, 5, 1, 11, 23, 455, 1, 1, 1, 85, 1, 133, 1, 275, 1, 23, 47, 455, 1, 1, 1, 145, 1, 2387, 1, 85, 23, 1, 71, 23350145, 1, 1, 1, 11275, 1, 2107, 431, 115, 1, 47, 1, 750295, 1, 11, 1, 265, 1, 133, 23, 145, 1, 59, 1, 47322275, 1, 1, 1, 85, 1, 10787, 1, 5, 47, 781, 1
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OFFSET
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1,4
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COMMENTS
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a(n) is a simple (the simplest?) example of a divisibility sequence associated to a rational point on an algebraic group of dimension larger than two. Specifically, it is the divisibility sequence associated to the point (2,3) on the two-dimensional torus G_m^2. Ailon and Rudnick conjecture that a(n) = 1 for infinitely many n.
According to Corvaja, a(n) < 2^n - 1 for all but finitely many n.
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REFERENCES
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Y. Bugeaud, P. Corvaja, U. Zannier, An upper bound for the G.C.D. of a^n-1 and b^n-1. Math. Z. 243 (2003), no. 1, 79-84
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LINKS
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FORMULA
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a(n) = gcd(2^n - 1, 3^n - 1).
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MAPLE
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MATHEMATICA
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PROG
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(PARI) vector(100, n, gcd(2^n-1, 3^n-1))
(Haskell)
a086892 n = a086892_list !! (n-1)
a086892_list = tail $ zipWith gcd a000225_list a003462_list
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Joseph H. Silverman (jhs(AT)math.brown.edu), Sep 18 2003
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EXTENSIONS
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Replaced arXiv URL with non-cached version by R. J. Mathar, Oct 23 2009
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STATUS
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approved
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