A191362 -id:A191362 - cp's OEIS frontend

A191360 Number of the diagonal of the Wythoff array that contains n.

0, 1, 2, -1, 3, -2, 0, 4, -3, -1, 1, -4, 5, -5, -2, 0, -6, 2, -7, -3, 6, -8, -4, -1, -9, 1, -10, -5, 3, -11, -6, -2, -12, 7, -13, -7, -3, -14, 0, -15, -8, 2, -16, -9, -4, -17, 4, -18, -10, -5, -19, -1, -20, -11, 8, -21, -12, -6, -22, -2, -23, -13, 1, -24, -14, -7, -25, 3, -26, -15, -8, -27, -3, -28, -16, 5, -29, -17, -9, -30

Offset: 1

Clark Kimberling, May 31 2011

sign

Every integer occurs in this sequence (infinitely many times).

Represent the array as {g(i,j): i>=1, j>=1}. Then for m>=0, (diagonal #m) is the sequence (g(i,i+m)), i>=1; for m<0, (diagonal #m) is the sequence (g(i+m,i)), i>=1.

			The main diagonal of the Wythoff array is (1,7,16,...); that's diagonal #0, so that a(1)=0, a(7)=0, a(16)=0.

Cf. A035513, A114327, A191361, A191362.

f[n_]:=f[n]=Fibonacci[n];
g[i_,j_]:=f[j+1]*Floor[i*GoldenRatio]+(i-1) f[j];
t=Table[g[i,j],{i,500},{j,100}];
Map[#[[2]]-#[[1]]&,Most[Reap[NestWhileList[#+1&,1,Length[Sow[FirstPosition[t,#]]]>1&]][[2]][[1]]]]  (* Peter J. C. Moses, Feb 09 2023 *)

Mathematica program replaced by Clark Kimberling, Feb 10 2023.

A191361 Number of the diagonal of the Wythoff difference array that contains n.

Original entry on oeis.org

0, 1, -1, -2, 2, -3, 0, -4, -5, -1, -6, -7, 3, -8, -2, -9, -10, 1, -11, -3, -12, -13, -4, -14, -15, 0, -16, -5, -17, -18, -6, -19, -20, 4, -21, -7, -22, -23, -1, -24, -8, -25, -26, -9, -27, -28, 2, -29, -10, -30, -31, -2, -32, -11, -33, -34, -12, -35, -36, -3

Offset: 1

Clark Kimberling, May 31 2011

sign

Every integer occurs in A191361 (infinitely many times).
Represent the array as {g(i,j): i>=1, j>=1}.  Then for m>=0, (diagonal #m) is the sequence (g(i,i+m)), i>=1;
for m<0, (diagonal #m) is the sequence (g(i+m,i)), i>=1.

			Diagonal #0 (the main diagonal) of A080164 is (1,7,26,...), so a(1)=0, a(7)=0, a(26)=0.

Cf. A080164, A114327, A191360, A191362.

r = GoldenRatio; f[n_] := Fibonacci[n];
g[i_, j_] := f[2 j - 1]*Floor[i*r] + (i - 1) f[2 j - 2];
TableForm[Table[g[i, j], {i, 1, 10}, {j, 1, 5}]]
(* A080164, Wythoff difference array *)
a = Flatten[Table[If[g[i, j] == n, j - i, {}], {n, 60}, {i, 50}, {j, 50}]]
(* a=A191361 *)

cp's OEIS Frontend

A191360 Number of the diagonal of the Wythoff array that contains n.

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