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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.
13
1, 5, 2, 13, 10, 3, 29, 26, 39, 4, 41, 58, 75, 20, 9, 61, 82, 147, 52, 21, 6, 85, 122, 207, 116, 45, 78, 7, 125, 170, 291, 164, 93, 150, 11, 8, 173, 250, 411, 244, 189, 294, 19, 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
OFFSET
1,2
COMMENTS
Alternative description: Each row r lists the positions of A019565(r) in A277330.
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.
All the terms on any particular row are either all multiples of two (or respectively: three, or six), or none of them are.
FORMULA
A(r,1) = A277711(r); for c > 1, A(r,c) = A277816(A(r,c-1)).
Other identities. For all r>=1, c>=1:
A(2*r,c) = 2*A(r,c).
A(r,c) modulo 4 = r modulo 4.
EXAMPLE
The top left 12 x 12 corner of the array:
1, 5, 13, 29, 41, 61, 85, 125, 173, 209, 253, 281
2, 10, 26, 58, 82, 122, 170, 250, 346, 418, 506, 562
3, 39, 75, 147, 207, 291, 411, 579, 819, 927, 1155, 1635
4, 20, 52, 116, 164, 244, 340, 500, 692, 836, 1012, 1124
9, 21, 45, 93, 189, 381, 657, 765, 873, 1317, 1533, 1749
6, 78, 150, 294, 414, 582, 822, 1158, 1638, 1854, 2310, 3270
7, 11, 19, 35, 67, 131, 259, 311, 359, 515, 619, 655
8, 40, 104, 232, 328, 488, 680, 1000, 1384, 1672, 2024, 2248
81, 105, 165, 213, 333, 429, 669, 861, 1341, 1725, 2685, 2721
18, 42, 90, 186, 378, 762, 1314, 1530, 1746, 2634, 3066, 3498
23, 43, 79, 83, 103, 155, 163, 203, 307, 323, 403, 611
12, 156, 300, 588, 828, 1164, 1644, 2316, 3276, 3708, 4620, 6540
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define (A277710 n) (A277710bi (A002260 n) (A004736 n)))
(define (A277710bi row col) (if (= 1 col) (A277711 row) (A277816 (A277710bi row (- col 1)))))
;; Alternatively:
(define (A277710bi row col) ((rowfun-for-A277710 row) col))
(definec (rowfun-for-A277710 n) (MATCHING-POS 1 0 (lambda (k) (= n (A264977 k)))))
CROSSREFS
Transpose: A277709.
Column 1: A277711, sorted into ascending order: A277817.
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.
Cf. A277824 (the index of the column where n is located in this array).
Cf. A019565, A264977, A277330, A277816 and permutation pair A277695 & A277696.
Sequence in context: A261327 A330613 A085436 * A286148 A369369 A194048
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Oct 29 2016
EXTENSIONS
The dispersion-style formula added by Antti Karttunen, Nov 06 2016
STATUS
approved