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A033953 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 x-axis.

%I A033953 #23 Aug 12 2018 21:26:57
%S A033953 0,7,1,7,4,2,8,1,1,3,1,2,0,2,3,1,3,4,6,5,5,5,7,7,8,8,9,6,8,1,1,1,2,3,
%T A033953 1,8,0,6,1,7,0,9,2,8,4,3,2,1,1,7,2,6,2,1,3,3,5,5,3,2,2,0,4,3,2,5,4,6,
%U A033953 5,0,5,1,1,6,5,8,1,2,6,7,3,8,7,8,9,5,7,1,8,2,8,6,1,9,9,3,6,7,9,0,1,4,6,1,0
%N A033953 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 x-axis.
%F A033953 a(n) = A033307(4*n^2 + 3*n - 1) for n > 0. - _Andrew Woods_, May 20 2012
%e A033953   2---3---2---4---2---5---2
%e A033953   |                       |
%e A033953   2   1---3---1---4---1   6
%e A033953   |   |               |   |
%e A033953   2   2   4---5---6   5   2
%e A033953   |   |   |       |   |   |
%e A033953   1   1   3   0   7   1   7
%e A033953   |   |   |   |   |   |   |
%e A033953   2   1   2---1   8   6   2
%e A033953   |   |           |   |   |
%e A033953   0   1---0---1---9   1   8
%e A033953   |                   |   |
%e A033953   2---9---1---8---1---7   2
%e A033953 We begin with the 0 and wrap the numbers 1 2 3 4 ... around it. Then the sequence is obtained by reading rightwards, starting from the initial 0. - _Andrew Woods_, May 20 2012
%t A033953 nmax = 105; A033307 = Flatten[IntegerDigits /@ Range[0, nmax^2 + 10 nmax]];
%t A033953 a[n_] := If[n==0, 0, A033307[[4n^2 + 3n + 1]]]; Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Apr 24 2017, after _Andrew Woods_ *)
%Y A033953 Sequences based on the same spiral: A033988, A033989, A033990. Spiral without zero: A033952.
%Y A033953 Other sequences from spirals: A001107, A002939, A007742, A033951, A033954, A033991, A002943, A033996, A033988.
%K A033953 nonn,base,easy,nice
%O A033953 0,2
%A A033953 _N. J. A. Sloane_
%E A033953 More terms from Andrew J. Gacek (andrew(AT)dgi.net)
%E A033953 Edited by _Charles R Greathouse IV_, Nov 01 2009