A097368 Least term in row n of the Fibonacci regression array in A097367.

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

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

Cf. A000032, A000045, A097367, A097369.

Sequence in context: A359539 A000119 A286326 * A271900 A194083 A109699

Adjacent sequences: A097365 A097366 A097367 * A097369 A097370 A097371

Keyword

nonn,look

Author

Clark Kimberling, Aug 09 2004

Extensions

a(46) = 6 inserted by Clark Kimberling, Oct 14 2016

Status

approved