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A097368
Least term in row n of the Fibonacci regression array in A097367.
4
1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 3, 1, 3, 3, 2, 4, 2, 3, 4, 1, 4, 3, 3, 5, 2, 4, 4, 2, 5, 3, 4, 5, 1, 5, 4, 3, 6, 3, 5, 5, 2, 6, 4, 4, 6, 2, 6, 5, 3, 7, 4, 5, 6, 1, 7, 5, 4, 7, 3, 6, 6, 3, 8, 5, 5, 7, 2, 7, 6, 4, 8, 4, 6, 7, 2, 8, 6, 5, 8, 3, 7, 7, 4, 9, 5, 6, 8, 1, 8, 7, 5, 9, 4, 7, 8, 3, 9, 6, 6, 9, 3, 8, 8, 5, 10, 5
OFFSET
2,3
COMMENTS
From Robert Israel, Jan 20 2018: (Start)
a(n) = 1 if and only if n is in A000045.
a(n) = 2 if and only if n >= 4 is in A000032 or 2*A000045.
a(m*n) <= m*a(n). (End)
LINKS
EXAMPLE
Row 8 of the array in A097367 is 7 6 5 4 1 4 6, of which the least term is T(8,5)=1.
MAPLE
T:= proc(n, k)
local s, t, u;
s:= n; t:= k;
do
u:= s-t;
if u <= 0 then return t fi;
s:= t;
t:= u;
od;
end proc:
f:= n -> min(seq(T(n, k), k=1..n-1)):
map(f, [$2..200]); # Robert Israel, Jan 19 2018
MATHEMATICA
f[n_] := Fibonacci[n]; d[n_, k_, 1] := n; d[n_, k_, 2] := k;
d[n_, k_, j_] := ((-1)^j) (k*f[j - 1] - n*f[j - 2]);
s[n_, k_] := Select[Range[100], d[n, k, # + 1] <= 0 &, 1];
t = Table[d[n, k, s[n, k]], {n, 2, 20}, {k, 1, n - 1}]; (* A097367 array *)
Flatten[t] (* A097367 sequence *)
Table[Min[Flatten[Table[d[n, k, s[n, k]], {k, 1, n - 1}]]], {n, 2, 100}] (* A097368 *)
(* Clark Kimberling, Oct 14 2016 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Clark Kimberling, Aug 09 2004
EXTENSIONS
a(46) = 6 inserted by Clark Kimberling, Oct 14 2016
STATUS
approved