login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1225; the first 49 antidiagonals of array

Index entries for sequences that are permutations of the natural numbers

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 A194048 A158868

Adjacent sequences:  A277707 A277708 A277709 * A277711 A277712 A277713

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Oct 29 2016

EXTENSIONS

The dispersion-style formula added by Antti Karttunen, Nov 06 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 7 09:46 EST 2021. Contains 341869 sequences. (Running on oeis4.)