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A033988 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 y-axis. 16
0, 5, 1, 4, 3, 7, 8, 0, 4, 7, 7, 1, 2, 6, 2, 1, 8, 7, 4, 2, 6, 1, 8, 9, 2, 7, 6, 0, 6, 5, 1, 2, 0, 4, 1, 5, 8, 5, 1, 8, 8, 8, 2, 1, 2, 3, 2, 4, 9, 0, 2, 8, 9, 9, 3, 3, 2, 0, 3, 7, 9, 3, 4, 2, 8, 8, 4, 7, 1, 5, 5, 3, 7, 4, 5, 9, 7, 5, 6, 5, 9, 8, 7, 1, 5, 3, 7, 8, 4, 0, 8, 5, 6, 9, 9, 3, 1, 0, 9, 8, 1, 1, 6, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In other words, write 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 ... in a clockwise spiral, starting with the 0 and taking the first step south; the sequence is then picked out from the resulting spiral by starting at the origin and moving north.

LINKS

Andrew Woods, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A033307(4*n^2 + n - 1) for n > 0. - Andrew Woods, May 18 2012

EXAMPLE

  1---3---1---4---1

  |               |

  2   4---5---6   5

  |   |       |   |

  1   3   0   7   1

  |   |   |   |   |

  1   2---1   8   6

  |           |   |

  1---0---1---9   1

.

We begin with the 0 and wrap the numbers 1 2 3 4 ... around it.

Then the sequence is obtained by reading vertically upwards, starting from the initial 0.

MATHEMATICA

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

CROSSREFS

Sequences based on the same spiral: A033953, A033989, A033990. Spiral without zero: A033952.

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

Cf. A033307.

Sequence in context: A010132 A254247 A216606 * A229200 A200421 A019977

Adjacent sequences:  A033985 A033986 A033987 * A033989 A033990 A033991

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

Edited by Jon E. Schoenfield, Aug 12 2018

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)