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A185586 EKG sequence (A064413) written clockwise as a square spiral and read counterclockwise.

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%I A185586 #28 Feb 16 2025 08:33:13
%S A185586 2,1,6,4,18,15,5,10,8,12,9,3,24,21,7,14,36,39,13,26,28,35,25,30,27,33,
%T A185586 11,22,20,16,38,42,51,17,34,32,58,70,65,55,60,63,49,56,54,52,50,48,69,
%U A185586 23,46,44,40,45,57,19,64,72,93,31,62,66,87,29,141,47,94,92,100
%N A185586 EKG sequence (A064413) written clockwise as a square spiral and read counterclockwise.
%C A185586 A permutation of the natural numbers.
%C A185586 The subsequence of primes (A000040) begins: 2, 5, 3, 7, 13, 11, 17, 23, 19, 31, 29, 47, 43, 41, 37, 53, ...
%H A185586 Alois P. Heinz, <a href="/A185586/b185586.txt">Table of n, a(n) for n = 1..10000</a>
%H A185586 J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0204011">The EKG sequence</a>, arXiv:math/0204011 [math.NT], 2002.
%H A185586 J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.3/Lagarias437_446.pdf">The EKG Sequence</a>, Exper. Math. 11 (2002), 437-446.
%H A185586 I. Peterson, <a href="http://www.maa.org/mathland/mathtrek_04_08_02.html">The EKG Sequence</a>
%H A185586 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EKGSequence.html">EKG Sequence</a>
%H A185586 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%H A185586 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A185586 1,2,4,6,3,9,12,8,10,5,15,18,... are written clockwise as a square spiral, then read counterclockwise: 2,1,6,4,18,15,5,10,8,12,9,3,...
%e A185586 The square spiral begins:
%e A185586 .
%e A185586   33--27--30--25--35--28
%e A185586    |                   |
%e A185586   11  12---8--10---5  26
%e A185586    |   |           |   |
%e A185586   22   9   1---2  15  13
%e A185586    |   |       |   |   |
%e A185586   20   3---6---4  18  39
%e A185586    |               |   |
%e A185586   16--24--21---7--14  36
%e A185586                        |
%e A185586   38--42--51--17--34--32
%Y A185586 Cf. A064413.
%K A185586 nonn,look
%O A185586 1,1
%A A185586 _Paul Curtz_, Feb 04 2011