OFFSET
1,1
COMMENTS
For n>=0, row n is the ordered sequence of positive integers m such that the number of even powers of 2 in the base 2 representation of m is n.
Every positive integer occurs exactly once in the array, so that as a sequence it is a permutation of the positive integers.
For odd powers, see A165275.
EXAMPLE
Northwest corner:
2....8...10...32...34...40...42...129
1....3....4....6....9...11...12...14
5....7...13...15...17...19...20...22
21..23...29...31...53...55...61...63
Examples:
40 = 32 + 8 = 2^5 + 2^3, so that 40 is in row 0.
13 = 8 + 4 + 1 = 2^3 + 2^2 + 2^0, so that 13 is in row 2.
MATHEMATICA
f[n_] := Total[(Reverse@IntegerDigits[n, 2])[[1 ;; -1 ;; 2]]]; T = GatherBy[ SortBy[Range[10^5], f], f]; Table[Table[T[[n - k + 1, k]], {k, n, 1, -1}], {n, 1, Length[T]}] // Flatten (* Amiram Eldar, Feb 04 2020*)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 12 2009
EXTENSIONS
More terms from Amiram Eldar, Feb 04 2020
STATUS
approved