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Search: id:A081459
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| A081459 |
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Consider the mapping f(r) = (1/2)*(r + N/r) from rationals to rationals where N = 5. Starting with r = 2 and applying the mapping to each new (reduced) rational number gives 2, 9/4, 161/72, 51841/23184, ..., tending to N^(1/2). Sequence gives values of the numerators. |
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3
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| 2, 9, 161, 51841, 5374978561, 57780789062419261441, 6677239169351578707225356193679818792961, 89171045849445921581733341920411050611581102638589828325078491812417901966295041
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Related sequence pairs (numerator, denominator) can be obtained by choosing N = 2, 3, 6 etc.
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FORMULA
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a(n)=a(n-1)^2+5*A081460(n-1)^2 - Mario Catalani (mario.catalani(AT)unito.it), May 21 2003
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PROGRAM
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(PARI) {r=2; N=5; for(n=1, 8, a=numerator(r); b=denominator(r); print1(a, ", "); r=(1/2)*(r + N/r) )}
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CROSSREFS
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Cf. A000129, A001333, A081460.
Sequence in context: A050995 A117116 A133468 this_sequence A038843 A053294 A078524
Adjacent sequences: A081456 A081457 A081458 this_sequence A081460 A081461 A081462
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
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