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 1-10 of 24 results. Next

A163337 Inverse permutation to A163336.

Original entry on oeis.org

0, 2, 5, 8, 4, 1, 3, 7, 12, 18, 25, 33, 26, 19, 13, 9, 14, 20, 27, 35, 44, 53, 43, 34, 42, 52, 63, 74, 62, 51, 61, 73, 86, 99, 85, 72, 60, 49, 39, 31, 40, 50, 41, 32, 24, 17, 11, 6, 10, 16, 23, 30, 22, 15, 21, 29, 38, 47, 37, 28, 36, 46, 57, 69, 82, 96, 83, 70, 58, 48, 59, 71
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

abs(A025581(a(n+1))-A025581(a(n))) + abs(A002262(a(n+1))-A002262(a(n))) = 1 for all n.

Links

Crossrefs

Inverse: A163336. a(n) = A163331(A163332(n)) = A061579(A163335(n)). One-based version: A163341. See also A163335, A163358.

A166043 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163357 as where n is located in the array A163336.

Original entry on oeis.org

0, 3, 4, 7, 2, 1, 14, 13, 8, 9, 54, 55, 56, 57, 6, 5, 58, 59, 60, 63, 64, 67, 62, 61, 50, 49, 68, 69, 48, 51, 46, 47, 122, 123, 44, 45, 34, 35, 28, 31, 32, 33, 52, 53, 10, 11, 12, 15, 16, 17, 30, 29, 18, 19, 20, 23, 24, 25, 22, 21, 234, 233, 230, 229, 218, 217, 38, 37, 26
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Comments

Fixed points are quite rare: A165467.

Examples

			The top left 9 X 9 corner of A163336:
   0  5  6 47 48 53 54 59 60
   1  4  7 46 49 52 55 58 61
   2  3  8 45 50 51 56 57 62
  15 14  9 44 39 38 69 68 63
  16 13 10 43 40 37 70 67 64
  17 12 11 42 41 36 71 66 65
  18 23 24 29 30 35 72 77 78
  19 22 25 28 31 34 73 76 79
  20 21 26 27 32 33 74 75 80
The top left 8 X 8 corner of A163357:
   0  1 14 15 16 19 20 21
   3  2 13 12 17 18 23 22
   4  7  8 11 30 29 24 25
   5  6  9 10 31 28 27 26
  58 57 54 53 32 35 36 37
  59 56 55 52 33 34 39 38
  60 61 50 51 46 45 40 41
  63 62 49 48 47 44 43 42
3 is in position (2,1) in A163336, while A163357(2,1) = 7. Thus a(3) = 7.

Links

Crossrefs

Inverse: A166044. a(n) = A163357(A163337(n)) = A163359(A163335(n)). Cf. also A166041.

A163480 Row 0 of A163334 (column 0 of A163336).

Original entry on oeis.org

0, 1, 2, 15, 16, 17, 18, 19, 20, 141, 142, 143, 144, 145, 146, 159, 160, 161, 162, 163, 164, 177, 178, 179, 180, 181, 182, 1275, 1276, 1277, 1278, 1279, 1280, 1293, 1294, 1295, 1296, 1297, 1298, 1311, 1312, 1313, 1314, 1315, 1316, 1437, 1438, 1439
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Crossrefs

Cf. A163481 (Y axis), A037314 (Z-order X axis).
Coordinates: A163528, A163529.

Programs

  • PARI
    a(n) = my(v=digits(n,3),s=Mod(0,2)); for(i=1,#v, if(s,v[i]+=6); s+=v[i]); fromdigits(v,9); \\ Kevin Ryde, Sep 29 2020

Formula

a(n) = A163332(A037314(n)). - Kevin Ryde, Sep 29 2020

A163481 Row 0 of A163336 (column 0 of A163334).

Original entry on oeis.org

0, 5, 6, 47, 48, 53, 54, 59, 60, 425, 426, 431, 432, 437, 438, 479, 480, 485, 486, 491, 492, 533, 534, 539, 540, 545, 546, 3827, 3828, 3833, 3834, 3839, 3840, 3881, 3882, 3887, 3888, 3893, 3894, 3935, 3936, 3941, 3942, 3947, 3948, 4313, 4314, 4319
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Crossrefs

Cf. A163480 (X axis), A208665 (Z-order Y axis).

Programs

  • PARI
    a(n) = my(v=digits(n,3),s=Mod(0,2)); for(i=1,#v, s+=v[i]; v[i]=3*v[i]+if(s,2)); fromdigits(v,9); \\ Kevin Ryde, Oct 06 2020

Formula

From Kevin Ryde, Oct 06 2020: (Start)
a(n) = A163332(A208665(n)), including at n=0 by reckoning A208665(0)=0.
a(n) = 3*A163480(n) + (2 if n odd).
(End)

A166044 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163336 as where n is located in the array A163357.

Original entry on oeis.org

0, 5, 4, 1, 2, 15, 14, 3, 8, 9, 44, 45, 46, 7, 6, 47, 48, 49, 52, 53, 54, 59, 58, 55, 56, 57, 68, 69, 38, 51, 50, 39, 40, 41, 36, 37, 70, 67, 66, 71, 72, 77, 76, 73, 34, 35, 30, 31, 28, 25, 24, 29, 42, 43, 10, 11, 12, 13, 16, 17, 18, 23, 22, 19, 20, 141, 140, 21, 26, 27, 134
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Examples

			The top left 8 X 8 corner of A163357:
   0  1 14 15 16 19 20 21
   3  2 13 12 17 18 23 22
   4  7  8 11 30 29 24 25
   5  6  9 10 31 28 27 26
  58 57 54 53 32 35 36 37
  59 56 55 52 33 34 39 38
  60 61 50 51 46 45 40 41
  63 62 49 48 47 44 43 42
The top left 9 X 9 corner of A163336:
   0  5  6 47 48 53 54 59 60
   1  4  7 46 49 52 55 58 61
   2  3  8 45 50 51 56 57 62
  15 14  9 44 39 38 69 68 63
  16 13 10 43 40 37 70 67 64
  17 12 11 42 41 36 71 66 65
  18 23 24 29 30 35 72 77 78
  19 22 25 28 31 34 73 76 79
  20 21 26 27 32 33 74 75 80
12 is in position (1,3) in A163357, while A163336(1,3) = 46. Thus a(12) = 46.

Links

Crossrefs

Inverse: A166043. a(n) = A163336(A163358(n)) = A163334(A163360(n)). Fixed points: A165467. Cf. also A166042.

A163342 Row sums of A163334 and A163336.

Original entry on oeis.org

0, 6, 12, 72, 132, 186, 240, 300, 360, 906, 1452, 1992, 2532, 3078, 3624, 4116, 4608, 5094, 5580, 6072, 6564, 7110, 7656, 8196, 8736, 9282, 9828, 14748, 19668, 24582, 29496, 34416, 39336, 44202, 49068, 53928, 58788, 63654, 68520, 73440, 78360
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

All terms seem to be divisible by 6. Cf. A163479.

A163343 Central diagonal of A163334 and A163336.

Original entry on oeis.org

0, 4, 8, 44, 40, 36, 72, 76, 80, 404, 400, 396, 360, 364, 368, 332, 328, 324, 648, 652, 656, 692, 688, 684, 720, 724, 728, 3644, 3640, 3636, 3600, 3604, 3608, 3572, 3568, 3564, 3240, 3244, 3248, 3284, 3280, 3276, 3312, 3316, 3320, 2996, 2992, 2988
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

It is easy to see by induction that these terms are always divisible by 4.

Crossrefs

Cf. A163344 (quarter), A128173, A163332, A163334, A338086.
Peano curve axes: A163480, A163481.

Programs

  • PARI
    a(n) = my(v=digits(n,3),s=Mod(0,2)); for(i=1,#v, if(s,v[i]=2-v[i]); s+=v[i]); fromdigits(v,9)<<2; \\ Kevin Ryde, Nov 06 2020

Formula

a(n) = 4*A163344(n).
a(n) = A163332(A338086(n)) = A338086(A128173(n)). - Kevin Ryde, Nov 06 2020

A163535 The absolute direction (0=east, 1=south, 2=west, 3=north) of the Peano curve A163336 at point n.

Original entry on oeis.org

1, 1, 0, 3, 3, 0, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 0, 3, 3, 0, 1, 1, 0, 3, 3, 0, 1, 1, 0, 3, 3, 3, 3, 3, 2, 1, 1, 2, 3, 3, 3, 3, 3, 0, 1, 1, 0, 3, 3, 0, 1, 1, 0, 3, 3, 0, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 0, 3, 3, 0, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 0, 3, 3, 0, 1, 1, 1, 1, 1, 2
Offset: 1

Views

Author

Antti Karttunen, Aug 01 2009

Keywords

Comments

Taking every ninth term gives the same sequence: (and similarly for all higher powers of 9 as well): a(n) = a(9*n).

Links

Crossrefs

Cf. A163534 (transposed), A163537 (turn).

Programs

Formula

a(n) = A010873(A163532(n)+A163533(n)+abs(A163532(n))+3).
a(n) = A004442(A163534(n)).

Extensions

Name corrected by Kevin Ryde, Aug 29 2020

A163537 The relative direction (0=straight ahead, 1=turn right, 2=turn left) of the Peano curve A163336 at point n.

Original entry on oeis.org

0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1
Offset: 1

Views

Author

Antti Karttunen, Aug 01 2009

Keywords

Comments

a(9*n) = a(81*n) for all n.

Links

Crossrefs

Cf. A163535 (direction), A163536 (transposed relative).

Programs

Formula

a(n) = A163241((A163535(n+1)-A163535(n)) modulo 4).
a(n) = A014681(A163536(n)).

Extensions

Name corrected by Kevin Ryde, Aug 29 2020

A163344 Central diagonal of A163334 and A163336 divided by 4.

Original entry on oeis.org

0, 1, 2, 11, 10, 9, 18, 19, 20, 101, 100, 99, 90, 91, 92, 83, 82, 81, 162, 163, 164, 173, 172, 171, 180, 181, 182, 911, 910, 909, 900, 901, 902, 893, 892, 891, 810, 811, 812, 821, 820, 819, 828, 829, 830, 749, 748, 747, 738, 739, 740, 731, 730, 729, 1458
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Crossrefs

a(n) = A163343(n)/4.
Showing 1-10 of 24 results. Next

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

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