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

1,2

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.

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

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)).

Example

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
  ...

Prog

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

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.

Sequence in context: A208613 A209584 A209140 * A345420 A364885 A006369

Adjacent sequences: A265900 A265901 A265902 * A265904 A265905 A265906

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 18 2015

Status

approved