A191361 -id:A191361 - 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.

A191362 Number of the diagonal of the dispersion of the even positive integers that contains n.

Original entry on oeis.org

0, -1, 1, -2, 2, 0, 3, -3, 4, 1, 5, -1, 6, 2, 7, -4, 8, 3, 9, 0, 10, 4, 11, -2, 12, 5, 13, 1, 14, 6, 15, -5, 16, 7, 17, 2, 18, 8, 19, -1, 20, 9, 21, 3, 22, 10, 23, -3, 24, 11, 25, 4, 26, 12, 27, 0, 28, 13, 29, 5, 30, 14, 31, -6, 32, 15, 33, 6, 34, 16, 35, 1, 36, 17, 37, 7, 38, 18, 39, -2, 40, 19, 41, 8, 42, 20, 43, 2, 44, 21, 45, 9, 46, 22, 47, -4, 48, 23, 49, 10

Offset: 1

Clark Kimberling, May 31 2011

sign

Every integer occurs in A191362 (infinitely many times).
Represent the array as {f(i,j): i>=1, j>=1}.  Then for m>=0, (diagonal #m) is the sequence (f(i,i+m)), i>=1;
for m<0, (diagonal #m) is the sequence (f(i+m,i)), i>=1.

Cf. A191362, A114327, A191360, A191361.

f[i_, j_] := (2 j - 1)*2^(i - 1);
t=TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 8}]]
(* t=A054582, the dispersion of the even positive integers *)
a = Flatten[Table[If[f[i, j] == n, j - i, {}], {n, 100}, {i, 10}, {j, 80}]]
(* a=A191362 *)

cp's OEIS Frontend

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

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