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

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

Author

Clark Kimberling, May 31 2011

Keywords

• sign

Comments

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.

Crossrefs

Cf. A191362, A114327, A191360, A191361.

Programs

Mathematica

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 *)