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A033988 Write 0,1,2,... in clockwise spiral, writing each digit in separate square; sequence gives numbers on 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

After one loop we have reached

456

307

218

After two loops we see

13141

24565

13071

12186

10191

and so on.

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, A033988.

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).

STATUS

approved

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Last modified February 20 15:54 EST 2018. Contains 299380 sequences. (Running on oeis4.)