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Search: id:A028941
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| A028941 |
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Denominator of X-coordinate of n*P where P is generator for rational points on curve y^2+y = x^3-x. |
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+0
2
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| 1, 1, 1, 1, 4, 1, 9, 25, 49, 16, 529, 841, 3481, 16641, 98596, 4225, 2337841, 13608721, 67387681, 264517696, 6941055969, 12925188721, 384768368209, 5677664356225, 61935294530404, 49020596163841, 16063784753682169
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OFFSET
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0,5
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COMMENT
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Squares of terms in A006769 (or A006720).
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REFERENCES
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G. Everest, A. J. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences: Examples and Applications, AMS Monographs, 2003
B. Mazur, Arithmetic on curves, Bull. Amer Math. Soc. 14 (1986), 207-259; see p 225.
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FORMULA
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This sequence satisfies the quadratic recurrence relation a(n)a(n-6)=-a(n-1)a(n-5)+2a(n-2)a(n-4)+2a(n-3)^2 which is a generalized Somos-6 relation. - Graham Everest (g.everest(AT)uea.ac.uk), Dec 16 2002
P=(0, 0), 2P=(1, 0), if kP=(a, b) then (k+1)P=(a'=(b^2-a^3)/a^2, b'=1-b*a'/a).
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CROSSREFS
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Sequence in context: A001254 A075150 A128626 this_sequence A065045 A064947 A059926
Adjacent sequences: A028938 A028939 A028940 this_sequence A028942 A028943 A028944
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KEYWORD
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nonn
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AUTHOR
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njas
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