cp's OEIS Frontend

A033989 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 x-axis.

%I A033989 #27 Aug 12 2018 21:27:03
%S A033989 0,3,1,1,3,2,7,9,1,1,6,9,4,7,9,1,2,1,2,1,6,7,4,3,6,1,2,9,5,1,1,0,9,3,
%T A033989 1,3,6,6,1,8,6,9,2,5,0,2,2,4,6,6,2,5,6,0,3,8,9,5,3,3,6,9,4,0,5,4,4,9,
%U A033989 8,0,5,0,4,5,5,3,3,1,6,8,5,8,6,5,1,4,7,4,9,1,8,5,1,9,9,8,6,6,9,1,1,6,4,8,1
%N A033989 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 x-axis.
%H A033989 Reinhard Zumkeller, <a href="/A033989/b033989.txt">Table of n, a(n) for n = 0..1000</a>
%F A033989 a(n) = A033307(4*n^2-n-1) for n > 0. - _Andrew Woods_, May 20 2012
%e A033989   2---3---2---4---2---5---2
%e A033989   |                       |
%e A033989   2   1---3---1---4---1   6
%e A033989   |   |               |   |
%e A033989   2   2   4---5---6   5   2
%e A033989   |   |   |       |   |   |
%e A033989   1   1   3   0   7   1   7
%e A033989   |   |   |   |   |   |   |
%e A033989   2   1   2---1   8   6   2
%e A033989   |   |           |   |   |
%e A033989   0   1---0---1---9   1   8
%e A033989   |                   |   |
%e A033989   2---9---1---8---1---7   2
%e A033989 We begin with the 0 and wrap the numbers 1 2 3 4 ... around it. Then the sequence is obtained by reading leftwards, starting from the initial 0. - _Andrew Woods_, May 20 2012
%t A033989 nmax = 1000; 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-François Alcover_, Apr 23 2017, after _Andrew Woods_ *)
%o A033989 (Haskell)
%o A033989 a033989 0 = 0
%o A033989 a033989 n = a033307 $ a185950 n  -- _Reinhard Zumkeller_, Aug 14 2013
%Y A033989 Sequences based on the same spiral: A033953, A033988, A033990. Spiral without zero: A033952.
%Y A033989 Other sequences from spirals: A001107, A002939, A007742, A033951, A033954, A033991, A002943, A033996, A033988.
%K A033989 nonn,base,easy,nice
%O A033989 0,2
%A A033989 _N. J. A. Sloane_
%E A033989 More terms from Andrew J. Gacek (andrew(AT)dgi.net)
%E A033989 Edited by _Charles R Greathouse IV_, Nov 01 2009