A228083 Table of binary Self-numbers and their descendants; square array T(r,c), with row r>=1, column c>=1, read by antidiagonals.

1, 2, 4, 3, 5, 6, 5, 7, 8, 13, 7, 10, 9, 16, 15, 10, 12, 11, 17, 19, 18, 12, 14, 14, 19, 22, 20, 21, 14, 17, 17, 22, 25, 22, 24, 23, 17, 19, 19, 25, 28, 25, 26, 27, 30, 19, 22, 22, 28, 31, 28, 29, 31, 34, 32, 22, 25, 25, 31, 36, 31, 33, 36, 36, 33, 37

Offset: 1

Author

Antti Karttunen, Aug 09 2013

Keywords

• nonn
• base
• tabl

Examples

			The top-left corner of the square array:
   1,  2,  3,  5,  7, 10, 12, 14, ...
   4,  5,  7, 10, 12, 14, 17, 19, ...
   6,  8,  9, 11, 14, 17, 19, 22, ...
  13, 16, 17, 19, 22, 25, 28, 31, ...
  15, 19, 22, 25, 28, 31, 36, 38, ...
  18, 20, 22, 25, 28, 31, 36, 38, ...
  21, 24, 26, 29, 33, 35, 38, 41, ...
  23, 27, 31, 36, 38, 41, 44, 47, ...
  ...
The non-initial terms on each row are obtained by adding to the preceding term the number of 1-bits in its binary representation (A000120).
		

Links

• Antti Karttunen, The first 141 antidiagonals of the table, flattened
• Index entries for Colombian or self numbers and related sequences

Crossrefs

First column: A010061. First row: A010062. Transpose: A228084. See A151942 for decimal analog.

Cf. also A000120, A092391, A227643, A228082, A228085, A228086, A228087, A228088, A228091, A218254.

Programs

Mathematica

nmax0 = 100;
nmax := Length[col[1]];
col[1] = Table[n + DigitCount[n, 2, 1], {n, 0, nmax0}] // Complement[Range[Last[#]], #]&;
col[k_] := col[k] = col[k - 1] + DigitCount[col[k-1], 2, 1];
T[n_, k_] := col[k][[n]];
Table[T[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Nov 28 2020 *)

Formula

T(r,1) are those numbers not of form n + sum of binary digits of n (binary Self numbers) = A010061(r);

T(r,c) = T(r,c-1) + sum of binary digits of T(r,c-1) = A092391(T(r,c-1)).