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A057677
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a(n) is the numerator of b(n) where b(n)=1/b(n-1)+1/b(n-2) with b(1)=1 and b(2)=2.
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3
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1, 2, 3, 7, 32, 339, 14287, 6877760, 143806067571, 1372321205281802503, 277081140489649960447116859520, 544875880027767543589801386360499677678401262339
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| lim_{n->infty} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/2)
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FORMULA
| a(n) satisfies the cubic recurrence : a(1)=1, a(2)=2, a(3)=3, a(4)=7, a(5)=32 and for n>=6 a(n)=a(n-2)^2*a(n-3)+a(n-1)*a(n-3)*a(n-4)
lim_{n->infty} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/2)
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CROSSREFS
| Cf. A066932.
Sequence in context: A096350 A018239 A066279 * A032148 A101484 A004026
Adjacent sequences: A057674 A057675 A057676 * A057678 A057679 A057680
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KEYWORD
| nonn,frac
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 24 2002
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EXTENSIONS
| Edited by Benoit Cloitre, Oct 25 2005
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