A033952 -id:A033952 - cp's OEIS frontend

A244690 The spiral of Champernowne read by the South-Southeast ray.

1, 1, 4, 8, 1, 1, 2, 4, 3, 4, 3, 7, 8, 8, 0, 1, 9, 6, 6, 1, 2, 7, 2, 2, 3, 2, 0, 3, 2, 9, 9, 4, 9, 9, 9, 5, 4, 1, 1, 6, 7, 7, 4, 7, 8, 5, 8, 9, 7, 6, 0, 6, 7, 1, 1, 1, 5, 8, 3, 1, 3, 4, 9, 5, 1, 5, 3, 0, 7, 1, 8, 2, 1, 9, 1, 0, 1, 2, 1, 2, 2, 0, 3, 4, 2, 5, 9, 4, 7, 2, 8, 8, 5, 0, 3, 1, 7, 6, 3, 3, 4, 6, 7, 6, 3

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A143839, A033952, A244677-A244688, A244691, A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 16n^2 - 25n + 10 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244692 The spiral of Champernowne read by the East-Southeast ray.

Original entry on oeis.org

1, 1, 0, 6, 1, 8, 2, 2, 9, 4, 5, 6, 7, 9, 0, 5, 3, 1, 5, 8, 2, 2, 1, 5, 9, 2, 9, 4, 4, 3, 8, 6, 7, 4, 8, 1, 8, 5, 9, 9, 7, 6, 2, 9, 4, 8, 6, 3, 9, 9, 0, 1, 0, 6, 7, 1, 1, 2, 5, 8, 3, 1, 4, 4, 9, 5, 1, 6, 3, 0, 7, 1, 8, 2, 1, 0, 2, 1, 1, 2, 2, 2, 3, 0, 3, 5, 2, 6, 9, 4, 8, 2, 9, 8, 5, 0, 3, 2, 7, 6, 4, 3, 5, 6, 7

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A143855, A033952, A244677-A244688, A244690, A244691.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 16n^2 - 39n + 24 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A033990 Write 0,1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 0 at the origin and 1 at x=0, y=-1; sequence gives the numbers on the negative y-axis.

Original entry on oeis.org

0, 1, 1, 8, 3, 7, 6, 2, 1, 5, 1, 1, 6, 2, 2, 1, 3, 4, 0, 4, 5, 3, 6, 7, 0, 8, 9, 1, 4, 6, 1, 2, 7, 1, 1, 4, 4, 8, 1, 7, 4, 7, 2, 0, 8, 8, 2, 4, 4, 1, 2, 8, 4, 6, 3, 2, 7, 3, 3, 7, 3, 2, 4, 1, 2, 3, 4, 7, 5, 6, 5, 2, 0, 1, 5, 8, 9, 8, 6, 4, 1, 7, 6, 1, 7, 8, 7, 7, 5, 1, 8, 4, 7, 6, 9, 2, 2, 3, 9, 0, 1, 0, 1, 6, 8

Offset: 0

N. J. A. Sloane

Consider array of digits 0_(1)23456789(1)0111213141516171(8)1920212223...; in this array add to n-th pointer 8*n+1 to get next pointer. E.g., n=1 so n+(8*1+1)=10 -> n=10 so n+(8*2+1)=27 -> n=27 so ... etc. - comment from Patrick De Geest.

			The spiral begins
                 2---3---2---4---2---5---2
                 |                       |
                 2   1---3---1---4---1   6
                 |   |               |   |
                 2   2   4---5---6   5   2
                 |   |   |       |   |   |
                 1   1   3   0   7   1   7
                 |   |   |   |   |   |   |
                 2   1   2---1   8   6   2
                 |   |           |   |   |
                 0   1---0---1---9   1   8
                 |                   |   |
                 2---9---1---8---1---7   2
                                         |
                             3---0---3---9
.
We begin with the 0 and wrap the numbers 1 2 3 4 ... around it. Then the sequence is obtained by reading downwards, starting from the initial 0. - _Andrew Woods_, May 20 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Sequences based on the same spiral: A033953, A033988, A033989. Spiral without zero: A033952.

Other sequences from spirals: A001107, A002939, A007742, A033951, A033954, A033991, A002943, A033996, A033988.

nmax = 105; A033307 = Flatten[IntegerDigits /@ Range[0, nmax^2 + 10 nmax]]; a[n_] := If[n==0, 0, A033307[[4n^2 - 3n + 1]]]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Apr 24 2017, after Andrew Woods *)

a(n) = A033307(4*n^2-3*n-1) for n > 0. - Andrew Woods, May 20 2012

More terms from Patrick De Geest, Oct 15 1999

Edited by Charles R Greathouse IV, Nov 01 2009

A033953 Write 0,1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 0 at the origin and 1 at x=0, y=-1; sequence gives the numbers on the positive x-axis.

Original entry on oeis.org

0, 7, 1, 7, 4, 2, 8, 1, 1, 3, 1, 2, 0, 2, 3, 1, 3, 4, 6, 5, 5, 5, 7, 7, 8, 8, 9, 6, 8, 1, 1, 1, 2, 3, 1, 8, 0, 6, 1, 7, 0, 9, 2, 8, 4, 3, 2, 1, 1, 7, 2, 6, 2, 1, 3, 3, 5, 5, 3, 2, 2, 0, 4, 3, 2, 5, 4, 6, 5, 0, 5, 1, 1, 6, 5, 8, 1, 2, 6, 7, 3, 8, 7, 8, 9, 5, 7, 1, 8, 2, 8, 6, 1, 9, 9, 3, 6, 7, 9, 0, 1, 4, 6, 1, 0

Offset: 0

N. J. A. Sloane

			  2---3---2---4---2---5---2
  |                       |
  2   1---3---1---4---1   6
  |   |               |   |
  2   2   4---5---6   5   2
  |   |   |       |   |   |
  1   1   3   0   7   1   7
  |   |   |   |   |   |   |
  2   1   2---1   8   6   2
  |   |           |   |   |
  0   1---0---1---9   1   8
  |                   |   |
  2---9---1---8---1---7   2
We begin with the 0 and wrap the numbers 1 2 3 4 ... around it. Then the sequence is obtained by reading rightwards, starting from the initial 0. - _Andrew Woods_, May 20 2012

Sequences based on the same spiral: A033988, A033989, A033990. Spiral without zero: A033952.

Other sequences from spirals: A001107, A002939, A007742, A033951, A033954, A033991, A002943, A033996, A033988.

nmax = 105; A033307 = Flatten[IntegerDigits /@ Range[0, nmax^2 + 10 nmax]];
a[n_] := If[n==0, 0, A033307[[4n^2 + 3n + 1]]]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Apr 24 2017, after Andrew Woods *)

a(n) = A033307(4*n^2 + 3*n - 1) for n > 0. - Andrew Woods, May 20 2012

More terms from Andrew J. Gacek (andrew(AT)dgi.net)

Edited by Charles R Greathouse IV, Nov 01 2009

A244691 The spiral of Champernowne read by the Southeast ray.

Original entry on oeis.org

1, 9, 7, 9, 5, 5, 9, 1, 1, 1, 3, 2, 2, 9, 3, 3, 9, 4, 4, 3, 5, 6, 1, 7, 8, 3, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 7, 7, 9, 3, 9, 0, 0, 3, 1, 1, 0

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A016754, A033952, A244677-A244688, A244690, A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 4n^2 - 4n + 1 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244678 The spiral of Champernowne read by the East-Northeast ray.

Original entry on oeis.org

1, 1, 2, 7, 5, 1, 2, 6, 3, 4, 3, 6, 7, 6, 0, 1, 1, 1, 5, 1, 2, 1, 1, 2, 1, 4, 9, 3, 8, 0, 8, 4, 3, 9, 8, 5, 6, 0, 0, 6, 7, 5, 2, 7, 6, 2, 6, 9, 3, 2, 0, 4, 1, 1, 4, 1, 2, 1, 1, 3, 3, 0, 1, 1, 2, 5, 0, 1, 1, 3, 7, 2, 1, 1, 6, 0, 6, 2, 2, 1, 2, 1, 2, 2, 7, 5, 8, 2, 2, 4, 8, 6, 2, 2, 4, 1, 6, 3, 3, 4, 4, 7, 3, 3, 7

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A143856, A244677 - A244688, A033952, A244690 - A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 16n^2 - 37n + 22 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244687 The spiral of Champernowne read by the Southwest ray.

Original entry on oeis.org

1, 7, 5, 6, 1, 0, 3, 1, 7, 1, 1, 5, 2, 2, 7, 3, 3, 3, 4, 5, 3, 6, 6, 7, 8, 8, 5, 0, 5, 1, 2, 2, 7, 3, 0, 5, 1, 6, 0, 8, 7, 9, 2, 1, 5, 3, 6, 5, 5, 7, 2, 9, 7, 1, 0, 3, 1, 5, 0, 7, 7, 0, 2, 2, 5, 5, 6, 8, 5, 0, 2, 3, 7, 6, 0, 9, 1, 2, 0, 5, 7, 8, 2, 2, 5, 5, 6, 8, 5, 2, 2, 6, 7, 9, 0, 3, 1, 7, 0, 0, 0, 4, 0, 5, 1

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A054569, A033952, A244677-A244688, A244690-A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 4n^2 - 6n + 3 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244679 The spiral of Champernowne read by the Northeast ray.

Original entry on oeis.org

1, 3, 1, 0, 3, 0, 1, 6, 1, 1, 3, 1, 2, 3, 2, 3, 7, 4, 4, 5, 5, 6, 7, 7, 7, 3, 9, 9, 7, 1, 2, 2, 5, 3, 6, 4, 5, 6, 2, 7, 7, 9, 0, 1, 1, 2, 0, 4, 7, 6, 2, 8, 5, 0, 6, 2, 5, 4, 2, 7, 7, 9, 0, 2, 1, 4, 0, 7, 7, 0, 2, 2, 5, 5, 6, 8, 5, 1, 2, 4, 7, 7, 0, 1, 1, 4, 0, 8, 7, 1, 2, 5, 5, 8, 6, 2, 5, 6, 2, 0, 0, 4, 0, 0, 8

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A054554, A244677 - A244688, A033952, A244690 - A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 4n^2 - 10n + 7 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244680 The spiral of Champernowne read by the North-Northeast ray.

Original entry on oeis.org

1, 1, 4, 7, 1, 6, 2, 9, 7, 4, 6, 7, 7, 2, 0, 6, 9, 1, 5, 0, 2, 2, 1, 7, 3, 2, 9, 7, 2, 3, 8, 9, 9, 4, 8, 5, 4, 5, 0, 3, 7, 6, 3, 4, 8, 8, 7, 7, 7, 9, 0, 4, 3, 1, 1, 1, 3, 4, 2, 1, 3, 2, 5, 4, 1, 5, 1, 6, 6, 1, 7, 0, 7, 9, 1, 0, 9, 8, 1, 2, 2, 8, 9, 4, 2, 5, 7, 0, 6, 2, 8, 6, 1, 9, 3, 1, 5, 2, 2, 3, 4, 4, 3, 6, 3

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A033952, A143861, A244677 - A244688, A244690 - A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 16n^2 - 35n + 20 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

A244681 The spiral of Champernowne read by the North ray.

Original entry on oeis.org

1, 4, 2, 2, 5, 5, 4, 1, 9, 1, 1, 4, 2, 2, 3, 3, 3, 6, 4, 5, 3, 6, 6, 4, 7, 8, 9, 1, 4, 1, 1, 1, 3, 5, 4, 1, 4, 3, 7, 1, 7, 4, 0, 2, 2, 9, 3, 2, 9, 6, 7, 2, 8, 7, 1, 3, 9, 1, 6, 3, 2, 8, 1, 4, 7, 8, 6, 4, 4, 2, 1, 5, 3, 8, 7, 5, 4, 8, 3, 6, 7, 1, 9, 7, 2, 8, 6, 7, 9, 7, 3, 8, 8, 0, 0, 9, 9, 6, 8, 0, 0, 2, 1, 8, 0

Offset: 1

Robert G. Wilson v, Jul 04 2014

			See A244677 for the spiral of David Gawen Champernowne.

Cf. A033307, A054556, A033952, A244677 - A244688, A244690 - A244692.

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 4n^2 - 9n + 6 (* see A244677 formula section *); Array[ almostNatural[ f@#, 10] &, 105]

See A244677 formula section.

cp's OEIS Frontend

A244690 The spiral of Champernowne read by the South-Southeast ray.

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A244692 The spiral of Champernowne read by the East-Southeast ray.

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A033990 Write 0,1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 0 at the origin and 1 at x=0, y=-1; sequence gives the numbers on the negative y-axis.

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A033953 Write 0,1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 0 at the origin and 1 at x=0, y=-1; sequence gives the numbers on the positive x-axis.

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A244691 The spiral of Champernowne read by the Southeast ray.

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A244678 The spiral of Champernowne read by the East-Northeast ray.

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A244687 The spiral of Champernowne read by the Southwest ray.

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A244679 The spiral of Champernowne read by the Northeast ray.

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A244680 The spiral of Champernowne read by the North-Northeast ray.

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