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 A080072 Values of n such that Pi^n is farther from its closest integer than any Pi^k for 1 <= k < n. 0
 1, 4, 8, 31, 61, 89, 200, 217, 257, 1366, 3642, 4926, 20265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS "Farthest from an integer" only really makes sense if we choose "nearest" or "farthest" integer. I chose nearest here. "Farthest from farthest" would just make "nearest to nearest" and would be sequence A080052. I think. LINKS Table of n, a(n) for n=1..13. EXAMPLE E.g., Pi^1=3.14159265... Pi^2=9.869..., Pi^3=31.00627..., Pi^4=97.40909... so Pi^4 is farther from 97 (its closest integer) than Pi^3 is from 31, or Pi^2 is from 10. MAPLE 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); PROG (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, Aug 22 2006 CROSSREFS Cf. A080052, A080053, A079490, A002160. Sequence in context: A248476 A082595 A262154 * A149091 A149092 A188117 Adjacent sequences: A080069 A080070 A080071 * A080073 A080074 A080075 KEYWORD nonn,more AUTHOR Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 24 2003 EXTENSIONS More terms from Robert Gerbicz, Aug 22 2006 STATUS approved

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Last modified December 1 14:40 EST 2023. Contains 367476 sequences. (Running on oeis4.)