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Search: id:A084764
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| A084764 |
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a(n)=2a(n-1)^2-1, a(0)=1, a(1)=4. |
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+0
2
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| 1, 4, 31, 1921, 7380481, 108942999582721, 23737154316161495960243527681, 1126904990058528673830897031906808442930637286502826475521
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Product((1+1/a(k)), k=1,..,n) converges to sqrt(5/3).
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REFERENCES
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H. S. Wilf, Limit of a sequence, Elementary Problem E 1093, Amer. Math. Monthly 61 (1954), 424-425
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LINKS
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J. O. Shallit, Rational numbers with non-terminating, non-periodic modified Engel-type expansions, Fib. Quart., 31 (1993), 37-40.
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FORMULA
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With a=4+sqrt(15), b=4-sqrt(15): a(n+1)=(a^(2^n)+b^(2^n))/2.
a(n)=A005828(n-1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
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MATHEMATICA
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For n>0: b[n_] := b[n] = 2 b[n - 1]^2 - 1; b[1] = 4 Table[b[n], {n, 1, 8}]
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CROSSREFS
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Sequence in context: A143077 A005841 A005828 this_sequence A061789 A103909 A068088
Adjacent sequences: A084761 A084762 A084763 this_sequence A084765 A084766 A084767
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jun 04 2003
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