A265903 Square array read by descending antidiagonals: A(1,k) = A188163(k), and for n > 1, A(n,k) = A087686(1+A(n-1,k)).

1, 3, 2, 5, 7, 4, 6, 12, 15, 8, 9, 14, 27, 31, 16, 10, 21, 30, 58, 63, 32, 11, 24, 48, 62, 121, 127, 64, 13, 26, 54, 106, 126, 248, 255, 128, 17, 29, 57, 116, 227, 254, 503, 511, 256, 18, 38, 61, 120, 242, 475, 510, 1014, 1023, 512, 19, 42, 86, 125, 247, 496, 978, 1022, 2037, 2047, 1024, 20, 45, 96, 192, 253, 502, 1006, 1992, 2046, 4084, 4095, 2048

Offset: 1

Author

Antti Karttunen, Dec 18 2015

Keywords

• nonn
• tabl

Comments

Square array A(n,k) [where n is row and k is column] is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

For n >= 3, each row n lists the numbers that appear n times in A004001. See also A051135.

Examples

			The top left corner of the array:
     1,    3,    5,    6,     9,    10,    11,    13,    17,    18,    19
     2,    7,   12,   14,    21,    24,    26,    29,    38,    42,    45
     4,   15,   27,   30,    48,    54,    57,    61,    86,    96,   102
     8,   31,   58,   62,   106,   116,   120,   125,   192,   212,   222
    16,   63,  121,  126,   227,   242,   247,   253,   419,   454,   469
    32,  127,  248,  254,   475,   496,   502,   509,   894,   950,   971
    64,  255,  503,  510,   978,  1006,  1013,  1021,  1872,  1956,  1984
   128,  511, 1014, 1022,  1992,  2028,  2036,  2045,  3864,  3984,  4020
   256, 1023, 2037, 2046,  4029,  4074,  4083,  4093,  7893,  8058,  8103
   512, 2047, 4084, 4094,  8113,  8168,  8178,  8189, 16006, 16226, 16281
  1024, 4095, 8179, 8190, 16292, 16358, 16369, 16381, 32298, 32584, 32650
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..210; the first 20 antidiagonals of array
• Index entries for Hofstadter-type sequences
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A267104.

Transpose: A265901.

Row 1: A188163.

Row 2: A266109.

Row 3: A267103.

For the known and suspected columns, see the rows listed for transposed array A265901.

Cf. A004001, A051135, A087686.

Cf. A265900 (main diagonal), A265909 (submain diagonal).

Cf. A162598 (column index of n in array), A265332 (row index of n in array).

Cf. also permutations A267111, A267112.

Programs

Scheme

(define (A265903 n) (A265903bi (A002260 n) (A004736 n)))
(define (A265903bi row col) (if (= 1 row) (A188163 col) (A087686 (+ 1 (A265903bi (- row 1) col)))))

Formula

For the first row n=1, A(1,k) = A188163(k), for rows n > 1, A(n,k) = A087686(1+A(n-1,k)).