A277898 Square array A(r,c), where each row r lists all numbers k for which A277892(k) = r, read by downwards antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

3, 4, 5, 6, 9, 7, 8, 12, 25, 11, 10, 14, 33, 49, 13, 18, 15, 35, 58, 93, 17, 22, 16, 44, 65, 119, 169, 19, 24, 20, 45, 77, 121, 185, 287, 23, 30, 21, 51, 91, 124, 209, 289, 361, 29, 32, 26, 55, 95, 143, 214, 299, 437, 529, 31, 40, 27, 57, 106, 161, 221, 323, 473, 589, 802, 37, 42, 28, 60, 111, 177, 247, 327, 493, 611, 841, 934, 41

Offset: 3

Author

Antti Karttunen, Nov 08 2016

Keywords

• nonn
• tabl

Comments

Permutation of natural numbers larger than 2.

Examples

			The top left corner of the array:
   3,    4,    6,    8,   10,   18,   22,   24,   30,   32
   5,    9,   12,   14,   15,   16,   20,   21,   26,   27
   7,   25,   33,   35,   44,   45,   51,   55,   57,   60
  11,   49,   58,   65,   77,   91,   95,  106,  111,  115
  13,   93,  119,  121,  124,  143,  161,  177,  187,  203
  17,  169,  185,  209,  214,  221,  247,  254,  301,  305
  19,  287,  289,  299,  323,  327,  391,  393,  398,  403
  23,  361,  437,  473,  493,  551,  565,  629,  633,  685
  29,  529,  589,  611,  667,  713,  779,  817,  889,  893
  31,  802,  841,  842,  851,  899,  901,  989, 1073, 1081
  37,  934,  961, 1121, 1147, 1154, 1189, 1227, 1271, 1293
  41, 1333, 1369, 1403, 1437, 1517, 1538, 1591, 1643, 1761
  43, 1681, 1739, 1763, 1927, 1943, 2183, 2257, 2263, 2302
  47, 1754, 1849, 2021, 2173, 2201, 2279, 2501, 2623, 2747
  53, 2209, 2491, 2537, 2594, 2643, 2701, 2773, 2881, 3053
		

Links

• Antti Karttunen, Table of n, a(n) for n = 3..353; the first 26 antidiagonals of array (computed from the b-file provided by _Hans Havermann_ for A277892)

Crossrefs

Transpose: A277897.

Row 1: A277319.

Column 1: A065091, column 2: A277900.

Cf. A277892 (index of the row where n is located), A277895 (of the column).

Cf. A001222, A048675, A277893.

Programs

Scheme

;; The terms for array proper start with A277898(3):
(define (A277898 n) (if (< n 3) n (A277898bi (A002260 (- n 2)) (A004736 (- n 2)))))
(define (A277898bi row col) (if (= 1 col) (A000040 (+ 1 row)) (A277893 (A277898bi row (- col 1)))))

Formula

A(r,1) = A065091(r); for c > 1, A(r,c) = A277893(A(r,c-1)).