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Search: id:A068119
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| A068119 |
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Number of steps to reach an integer starting with n + 1/4 and iterating the map x -> x*ceiling(x). |
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+0
12
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| 3, 3, 1, 3, 2, 2, 1, 7, 4, 4, 1, 2, 2, 4, 1, 6, 3, 5, 1, 5, 2, 2, 1, 4, 6, 3, 1, 2, 2, 3, 1, 7, 3, 4, 1, 3, 2, 2, 1, 7, 4, 7, 1, 2, 2, 5, 1, 3, 3, 10, 1, 4, 2, 2, 1, 3, 5, 11, 1, 2, 2, 3, 1, 5, 3, 3, 1, 3, 2, 2, 1, 4, 4, 6, 1, 2, 2, 4, 1, 4, 3, 6, 1, 6, 2, 2, 1, 6, 7, 3, 1, 2, 2, 3, 1, 4, 3, 5, 1, 3, 2, 2, 1, 4
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If the initial value is n + 1/2 we get A001511.
S(n)=sum(k=1, n, a(k)) seems to be asymptotic to 3*n. S(n)=3n for in A074069.
The sign of 3n-S(n) seems to change often: 3n-S(n) gives A074077. Is 3n-S(n) bounded? - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 05 2002
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LINKS
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J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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FORMULA
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a(n) = 1 if n == 3 (mod 4); a(n) = 2 if n == 5, 6, 12, 13 (mod 16); a(n) = 3 if n == 1, 2, 4, 17, 26, 30, 33, 36, 48, 49, 56, 62 (mod 64);...
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=n+1/4; c=0; while(frac(s)>0, s=s*ceil(s); c++); c)
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CROSSREFS
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Cf. A073524, A074069, A074077
Adjacent sequences: A068116 A068117 A068118 this_sequence A068120 A068121 A068122
Sequence in context: A124330 A055177 A030778 this_sequence A039992 A101988 A088420
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2002
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EXTENSIONS
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Corrected by Diego Torres (torresvillarroel(AT)hotmail.com), Aug 31 2002
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