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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. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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.

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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-Fran├žois Alcover, Apr 24 2017, after Andrew Woods *)

CROSSREFS

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.

Sequence in context: A206161 A131654 A241243 * A248190 A099284 A061444

Adjacent sequences:  A033987 A033988 A033989 * A033991 A033992 A033993

KEYWORD

nonn,base,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Patrick De Geest, Oct 15 1999

Edited by Charles R Greathouse IV, Nov 01 2009

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)