

A086892


Greatest common divisor of 2^n1 and 3^n1.


7



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

1,4


COMMENTS

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 twodimensional 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.


REFERENCES

Y. Bugeaud, P. Corvaja, U. Zannier, An upper bound for the G.C.D. of a^n1 and b^n1. Math. Z. 243 (2003), no. 1, 7984


LINKS



FORMULA

a(n) = gcd(2^n  1, 3^n  1).


MAPLE



MATHEMATICA



PROG

(PARI) vector(100, n, gcd(2^n1, 3^n1))
(Haskell)
a086892 n = a086892_list !! (n1)
a086892_list = tail $ zipWith gcd a000225_list a003462_list


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

Joseph H. Silverman (jhs(AT)math.brown.edu), Sep 18 2003


EXTENSIONS

Replaced arXiv URL with noncached version by R. J. Mathar, Oct 23 2009


STATUS

approved



