

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 yaxis.


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

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.
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.
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



