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Search: id:A086892
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| A086892 |
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Greatest common divisor of 2^n-1 and 3^n-1. |
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+0
4
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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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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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.
a(n)=GCD(A000255(n), A003462(n))=GCD(A000255(n), A024023(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2004
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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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N. Ailon, Z. Rudnick, Torsion points on curves and common divisors of a^k-1 and b^k-1, Acta Arith. 113 (2004), no. 1, 31-38.
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FORMULA
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a(n) = gcd(2^n - 1, 3^n - 1)
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PROGRAM
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(PARI) vector(100, n, gcd(2^n-1, 3^n-1))
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CROSSREFS
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Sequence in context: A068328 A109375 A051712 this_sequence A089027 A023890 A102778
Adjacent sequences: A086889 A086890 A086891 this_sequence A086893 A086894 A086895
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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 by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009
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