cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A277320 Square array A(r,c) = A048720(A065621(r), c), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 2, 2, 3, 4, 7, 4, 6, 14, 4, 5, 8, 9, 8, 13, 6, 10, 28, 12, 26, 14, 7, 12, 27, 16, 23, 28, 11, 8, 14, 18, 20, 52, 18, 22, 8, 9, 16, 21, 24, 57, 56, 29, 16, 25, 10, 18, 56, 28, 46, 54, 44, 24, 50, 26, 11, 20, 63, 32, 35, 36, 39, 32, 43, 52, 31, 12, 22, 54, 36, 104, 42, 58, 40, 100, 46, 62, 28, 13, 24, 49, 40, 101, 112, 49, 48, 125, 104, 33, 56, 21
Offset: 1

Views

Author

Antti Karttunen, Nov 01 2016

Keywords

Examples

			The top left corner of the array:
   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12
   2,   4,   6,   8,  10,  12,  14,  16,  18,  20,  22,  24
   7,  14,   9,  28,  27,  18,  21,  56,  63,  54,  49,  36
   4,   8,  12,  16,  20,  24,  28,  32,  36,  40,  44,  48
  13,  26,  23,  52,  57,  46,  35, 104, 101, 114, 127,  92
  14,  28,  18,  56,  54,  36,  42, 112, 126, 108,  98,  72
  11,  22,  29,  44,  39,  58,  49,  88,  83,  78,  69, 116
   8,  16,  24,  32,  40,  48,  56,  64,  72,  80,  88,  96
  25,  50,  43, 100, 125,  86,  79, 200, 209, 250, 227, 172
  26,  52,  46, 104, 114,  92,  70, 208, 202, 228, 254, 184
  31,  62,  33, 124,  99,  66,  93, 248, 231, 198, 217, 132
  28,  56,  36, 112, 108,  72,  84, 224, 252, 216, 196, 144
  21,  42,  63,  84,  65, 126, 107, 168, 189, 130, 151, 252
  22,  44,  58,  88,  78, 116,  98, 176, 166, 156, 138, 232
  19,  38,  53,  76,  95, 106, 121, 152, 139, 190, 173, 212
  16,  32,  48,  64,  80,  96, 112, 128, 144, 160, 176, 192
  49,  98,  83, 196, 245, 166, 151, 392, 441, 490, 475, 332
  50, 100,  86, 200, 250, 172, 158, 400, 418, 500, 454, 344
  55, 110,  89, 220, 235, 178, 133, 440, 399, 470, 481, 356

Links

Crossrefs

Transpose: A277199.
Main diagonal: A277699.
Row 1: A000027, Row 3: A048727.
Column 1: A065621, Column 3: A277823, Column 5: A277825.
Cf. A277820 (array obtained by selecting only the columns with an index A001317(k), k=0..).
Cf. A048720, A115872.

Programs

Formula

A(r,c) = A048720(A065621(r), c).

A277820 Square array: A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 3, 2, 5, 6, 7, 15, 10, 9, 4, 17, 30, 27, 12, 13, 51, 34, 45, 20, 23, 14, 85, 102, 119, 60, 57, 18, 11, 255, 170, 153, 68, 75, 54, 29, 8, 257, 510, 427, 204, 221, 90, 39, 24, 25, 771, 514, 765, 340, 359, 238, 105, 40, 43, 26, 1285, 1542, 1799, 1020, 937, 306, 187, 120, 125, 46, 31, 3855, 2570, 2313, 1028, 1275, 854, 461, 136, 135, 114, 33, 28
Offset: 1

Views

Author

Antti Karttunen, Nov 01 2016

Keywords

Comments

For all n >= 1, A277818 (= A268389(n)+1) gives the (one-based) index of the column where n is located in this array, while A268671(n) gives the (one-based) index of the row where it is on.
This array is obtained when one selects from A277320 the columns 1, 3, 5, 15, 17, 51, ..., i.e., those with an index A001317(k).

Examples

			The top left corner of the array:
   1,  3,   5,  15,  17,   51,   85,  255,   257,   771,  1285,  3855
   2,  6,  10,  30,  34,  102,  170,  510,   514,  1542,  2570,  7710
   7,  9,  27,  45, 119,  153,  427,  765,  1799,  2313,  6939, 11565
   4, 12,  20,  60,  68,  204,  340, 1020,  1028,  3084,  5140, 15420
  13, 23,  57,  75, 221,  359,  937, 1275,  3341,  5911, 14649, 19275
  14, 18,  54,  90, 238,  306,  854, 1530,  3598,  4626, 13878, 23130
  11, 29,  39, 105, 187,  461,  599, 1785,  2827,  7453, 10023, 26985
   8, 24,  40, 120, 136,  408,  680, 2040,  2056,  6168, 10280, 30840
  25, 43, 125, 135, 393,  667, 1965, 2295,  6425, 11051, 32125, 34695
  26, 46, 114, 150, 442,  718, 1874, 2550,  6682, 11822, 29298, 38550
  31, 33,  99, 165, 495,  561, 1619, 2805,  7967,  8481, 25443, 42405
  28, 36, 108, 180, 476,  612, 1708, 3060,  7196,  9252, 27756, 46260
  21, 63,  65, 195, 325,  975, 1105, 3315,  5397, 16191, 16705, 50115
  22, 58,  78, 210, 374,  922, 1198, 3570,  5654, 14906, 20046, 53970
  19, 53,  95, 225, 291,  869, 1455, 3825,  4883, 13621, 24415, 57825
  16, 48,  80, 240, 272,  816, 1360, 4080,  4112, 12336, 20560, 61680
  49, 83, 245, 287, 801, 1379, 4005, 4335, 12593, 21331, 62965, 73247
  50, 86, 250, 270, 786, 1334, 3930, 4590, 12850, 22102, 64250, 69390
  55, 89, 235, 317, 839, 1481, 3675, 4845, 14135, 22873, 60395, 80957

Links

Crossrefs

Inverse permutation: A277821.
Transpose: A277819.
Cf. A048724, A065621.
Row 1: A001317.
Column 1: A065621, column 2: A277823, column 3: A277825.
Cf. A268389, A277818, A268671.
Cf. also A193231, A277320, A277810, A276618 (A099884), A248513.
Other related tables or permutations: A277880, A277901.

Programs

Formula

A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)).
A(r,c) = A048675(A277810(r,c)).
As a composition of other permutations:
a(n) = A277901(A277880(n)).

A277902 If A010060(n) = 1, a(n) = A000069(A268671(n)), otherwise a(n) = A001969(1+a(A006068(n)/2)).

Original entry on oeis.org

1, 2, 3, 7, 6, 5, 4, 14, 9, 10, 13, 15, 8, 11, 12, 31, 24, 23, 28, 30, 25, 26, 17, 29, 16, 19, 18, 22, 27, 20, 21, 62, 43, 40, 61, 45, 56, 59, 54, 58, 49, 50, 33, 55, 36, 39, 52, 63, 32, 35, 48, 38, 57, 46, 37, 47, 34, 53, 44, 60, 41, 42, 51, 127, 102, 85, 124, 120, 121, 122, 83, 95, 112, 115, 68, 118, 89, 106
Offset: 1

Views

Author

Antti Karttunen, Nov 03 2016

Keywords

Comments

a(n) gives the number that is in the same position in array A277880 as where n is located in array A277820.

Examples

			The top left corner of array A277820 is:
   1,  3,  5, 15
   2,  6, 10, 30
   7,  9, 27, 45
   4, 12, 20, 60
  13, 23, 57, 75
while the top left corner of A277880 is:
   1,  3,  6, 12
   2,  5, 10, 20
   4,  9, 18, 36
   7, 15, 30, 60
   8, 17, 34, 68
thus for example, a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 7, a(5) = 6, a(6) = 5, a(7) = 4, a(9) = 9, a(12) = 15, a(13) = 8 and a(27) = 18.

Links

Crossrefs

Inverse: A277901.
Cf. A000069, A001969, A001317, A003945, A006068, A010060, A065621, A129771, A268671, A277823, A277825.
Related permutations and arrays: A277820, A277821, A277880.

Formula

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = A000069(A268671(n)), otherwise a(n) = A001969(1+a(A006068(n)/2)).
As a composition of other permutations:
a(n) = A277880(A277821(n)).
Other identities. For all n >= 1:
A010060(a(n)) = A010060(n). [Preserves the parity of binary weight.]
a(A001317(n)) = A003945(n).
a(A065621(n)) = A000069(n).
a(A277823(n)) = A129771(n).
a(A277825(n)) = 2*A129771(n).

A277901 If A010060(n) = 1, a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).

Original entry on oeis.org

1, 2, 3, 7, 6, 5, 4, 13, 9, 10, 14, 15, 11, 8, 12, 25, 23, 27, 26, 30, 31, 28, 18, 17, 21, 22, 29, 19, 24, 20, 16, 49, 43, 57, 50, 45, 55, 52, 46, 34, 61, 62, 33, 59, 36, 54, 56, 51, 41, 42, 63, 47, 58, 39, 44, 37, 53, 40, 38, 60, 35, 32, 48, 97, 83, 125, 98, 75, 103, 100, 86, 119, 109, 110, 89, 107, 92, 114
Offset: 1

Views

Author

Antti Karttunen, Nov 03 2016

Keywords

Comments

a(n) gives the number that is in the same position in array A277820 as where n is located in array A277880.

Examples

			The top left corner of array A277880 is:
   1,  3,  6, 12
   2,  5, 10, 20
   4,  9, 18, 36
   7, 15, 30, 60
   8, 17, 34, 68
while the top left corner of A277820 is:
   1,  3,  5, 15
   2,  6, 10, 30
   7,  9, 27, 45
   4, 12, 20, 60
  13, 23, 57, 75
thus a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 7, a(5) = 6, a(6) = 5, a(7) = 4, a(8) = 13, a(9) = 9, a(12) = 15 and a(15) = 12.

Links

Crossrefs

Inverse: A277902.
Cf. A000069, A001969, A010060, A048724, A065621, A115384, A129771, A277823, A277825.
Related permutations and arrays: A277820, A277880, A277881.

Formula

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).
As a composition of other permutations:
a(n) = A277820(A277881(n)).
Other identities. For all n >= 1:
A010060(a(n)) = A010060(n). [Preserves the parity of binary weight.]
a(A000069(n)) = A065621(n).
a(A003945(n)) = A001317(n).
a(A129771(n)) = A277823(n).
a(2*A129771(n)) = A277825(n).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.