A080072 Values of n such that Pi^n is farther from its closest integer than any Pi^k for 1 <= k < n.

1, 4, 8, 31, 61, 89, 200, 217, 257, 1366, 3642, 4926, 20265

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