OFFSET
2,3
COMMENTS
From Robert Israel, Jan 20 2018: (Start)
a(n) = 1 if and only if n is in A000045.
a(m*n) <= m*a(n). (End)
LINKS
Robert Israel, Table of n, a(n) for n = 2..10000
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