

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
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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+n1) for n > 0.  Andrew Woods, May 18 2012


EXAMPLE

..13141..
...........
..2.456.5..
.........
..1.3.0.7.1..
........
..1.21.8.6..
..........
..1019.1..
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}] (* JeanFrançois 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



