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A277710 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.

%I A277710 #27 Nov 07 2016 09:10:42
%S A277710 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 A277710 116,45,78,7,125,170,291,164,93,150,11,8,173,250,411,244,189,294,19,
%U A277710 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 A277710 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 A277710 Alternative description: Each row r lists the positions of A019565(r) in A277330.
%C A277710 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 A277710 All the terms on any particular row are either all multiples of two (or respectively: three, or six), or none of them are.
%H A277710 Antti Karttunen, <a href="/A277710/b277710.txt">Table of n, a(n) for n = 1..1225; the first 49 antidiagonals of array</a>
%H A277710 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A277710 A(r,1) = A277711(r); for c > 1, A(r,c) = A277816(A(r,c-1)).
%F A277710 Other identities. For all r>=1, c>=1:
%F A277710 A(2*r,c) = 2*A(r,c).
%F A277710 A(r,c) modulo 4 = r modulo 4.
%e A277710 The top left 12 x 12 corner of the array:
%e A277710    1,   5,  13,  29,  41,   61,   85,  125,  173,  209,  253,  281
%e A277710    2,  10,  26,  58,  82,  122,  170,  250,  346,  418,  506,  562
%e A277710    3,  39,  75, 147, 207,  291,  411,  579,  819,  927, 1155, 1635
%e A277710    4,  20,  52, 116, 164,  244,  340,  500,  692,  836, 1012, 1124
%e A277710    9,  21,  45,  93, 189,  381,  657,  765,  873, 1317, 1533, 1749
%e A277710    6,  78, 150, 294, 414,  582,  822, 1158, 1638, 1854, 2310, 3270
%e A277710    7,  11,  19,  35,  67,  131,  259,  311,  359,  515,  619,  655
%e A277710    8,  40, 104, 232, 328,  488,  680, 1000, 1384, 1672, 2024, 2248
%e A277710   81, 105, 165, 213, 333,  429,  669,  861, 1341, 1725, 2685, 2721
%e A277710   18,  42,  90, 186, 378,  762, 1314, 1530, 1746, 2634, 3066, 3498
%e A277710   23,  43,  79,  83, 103,  155,  163,  203,  307,  323,  403,  611
%e A277710   12, 156, 300, 588, 828, 1164, 1644, 2316, 3276, 3708, 4620, 6540
%o A277710 (Scheme, with Antti Karttunen's IntSeq-library)
%o A277710 (define (A277710 n) (A277710bi (A002260 n) (A004736 n)))
%o A277710 (define (A277710bi row col) (if (= 1 col) (A277711 row) (A277816 (A277710bi row (- col 1)))))
%o A277710 ;; Alternatively:
%o A277710 (define (A277710bi row col) ((rowfun-for-A277710 row) col))
%o A277710 (definec (rowfun-for-A277710 n) (MATCHING-POS 1 0 (lambda (k) (= n (A264977 k)))))
%Y A277710 Transpose: A277709.
%Y A277710 Column 1: A277711, sorted into ascending order: A277817.
%Y A277710 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 A277710 Cf. A277824 (the index of the column where n is located in this array).
%Y A277710 Cf. A019565, A264977, A277330, A277816 and permutation pair A277695 & A277696.
%K A277710 nonn,tabl
%O A277710 1,2
%A A277710 _Antti Karttunen_, Oct 29 2016
%E A277710 The dispersion-style formula added by _Antti Karttunen_, Nov 06 2016