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Search: id:A080072
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| A080072 |
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Values of n such that pi^n is further from its closest integer than any pi^k for 1 <= k < n. |
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+0
1
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| 1, 4, 8, 31, 61, 89, 200, 217, 257, 1366, 3642, 4926, 20265
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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"Furthest from an integer" only really makes sense if we choose "nearest" or "furthest" integer. I chose nearest here. "Furthest from furthest" would just make "nearest to nearest" and would be sequence A080052. I think.
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EXAMPLE
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e.g. pi^1=3.14159265... pi^2=9.869..., pi^3=31.00627..., pi^4=97.40909... so pi^4 is further from 97 (its closest integer) than pi^3 is to 31, or pi^2 is to 10.
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MAPLE
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b := array(1..5000): Digits := 10000: c := 0: pos := 0: for n from 1 to 10000 do: exval := evalf(Pi^n): if (abs(exval-round(exval))>c) then c := (abs(exval-round(exval))): pos := pos+1: b[pos] := n: print(n):fi: od: seq(b[n], n=1..pos);
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PROGRAM
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(PARI) default(realprecision, 20000); d=0.0; p=Pi; a=1; for(n=1, 40000, a*=p; s=abs(a-round(a)); if(s>d, d=s; print1(n, ", "))) - Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 22 2006
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CROSSREFS
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Cf. A080052, A080053, A079490, A002160.
Sequence in context: A075308 A020331 A082595 this_sequence A149091 A149092 A094502
Adjacent sequences: A080069 A080070 A080071 this_sequence A080073 A080074 A080075
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KEYWORD
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nonn
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AUTHOR
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Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 24 2003
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EXTENSIONS
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More terms from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 22 2006
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