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%I #27 Nov 07 2016 09:10:42
%S 1,5,2,13,10,3,29,26,39,4,41,58,75,20,9,61,82,147,52,21,6,85,122,207,
%T 116,45,78,7,125,170,291,164,93,150,11,8,173,250,411,244,189,294,19,
%U 40,81,209,346,579,340,381,414,35,104,105,18,253,418,819,500,657,582,67,232,165,42,23,281,506,927,692,765,822,131,328,213,90,43,12
%N Square array A(r,c), where each row r lists all numbers k for which A264977(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.
%C Alternative description: Each row r lists the positions of A019565(r) in A277330.
%C Odd terms occur only on rows with odd index, and even terms only on rows with even index. Specifically: all terms k on row r are equal to r modulo 4, thus the first differences of each row are all multiples of 4.
%C All the terms on any particular row are either all multiples of two (or respectively: three, or six), or none of them are.
%H Antti Karttunen, <a href="/A277710/b277710.txt">Table of n, a(n) for n = 1..1225; the first 49 antidiagonals of array</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A(r,1) = A277711(r); for c > 1, A(r,c) = A277816(A(r,c-1)).
%F Other identities. For all r>=1, c>=1:
%F A(2*r,c) = 2*A(r,c).
%F A(r,c) modulo 4 = r modulo 4.
%e The top left 12 x 12 corner of the array:
%e 1, 5, 13, 29, 41, 61, 85, 125, 173, 209, 253, 281
%e 2, 10, 26, 58, 82, 122, 170, 250, 346, 418, 506, 562
%e 3, 39, 75, 147, 207, 291, 411, 579, 819, 927, 1155, 1635
%e 4, 20, 52, 116, 164, 244, 340, 500, 692, 836, 1012, 1124
%e 9, 21, 45, 93, 189, 381, 657, 765, 873, 1317, 1533, 1749
%e 6, 78, 150, 294, 414, 582, 822, 1158, 1638, 1854, 2310, 3270
%e 7, 11, 19, 35, 67, 131, 259, 311, 359, 515, 619, 655
%e 8, 40, 104, 232, 328, 488, 680, 1000, 1384, 1672, 2024, 2248
%e 81, 105, 165, 213, 333, 429, 669, 861, 1341, 1725, 2685, 2721
%e 18, 42, 90, 186, 378, 762, 1314, 1530, 1746, 2634, 3066, 3498
%e 23, 43, 79, 83, 103, 155, 163, 203, 307, 323, 403, 611
%e 12, 156, 300, 588, 828, 1164, 1644, 2316, 3276, 3708, 4620, 6540
%o (Scheme, with Antti Karttunen's IntSeq-library)
%o (define (A277710 n) (A277710bi (A002260 n) (A004736 n)))
%o (define (A277710bi row col) (if (= 1 col) (A277711 row) (A277816 (A277710bi row (- col 1)))))
%o ;; Alternatively:
%o (define (A277710bi row col) ((rowfun-for-A277710 row) col))
%o (definec (rowfun-for-A277710 n) (MATCHING-POS 1 0 (lambda (k) (= n (A264977 k)))))
%Y Transpose: A277709.
%Y Column 1: A277711, sorted into ascending order: A277817.
%Y Row 1: A277701, Row 2: A277712 (= 2*A277701), Row 3: A277713, Row 4: 4*A277701, Row 5: A277715, Row 6: 2*A277713. Row 8: 8*A277701, Row 10: 2*A277715.
%Y Cf. A277824 (the index of the column where n is located in this array).
%Y Cf. A019565, A264977, A277330, A277816 and permutation pair A277695 & A277696.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Oct 29 2016
%E The dispersion-style formula added by _Antti Karttunen_, Nov 06 2016
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