|
%I #35 Nov 02 2023 14:19:11
%S 1,2,5,3,10,4,14,8,6,9,20,7,28,13,11,17,33,12,37,18,15,19,43,16,24,27,
%T 22,26,57,23,61,31,21,32,25,30,67,36,29,40,74,35,81,41,39,42,89,45,50,
%U 46,34,47,100,48,53,49,38,56,107,52,115,60,51,64,54,59,128,65,44,55
%N Regard A064413 as giving a permutation of the positive integers; sequence gives inverse permutation.
%C The Mathematica program computes the EKG sequence A064413 and then determines the inverse permutation. - _T. D. Noe_, Nov 13 2002
%H Ray Chandler, <a href="/A064664/b064664.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H J. C. Lagarias, E. M. Rains, and N. J. A. Sloane, <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-3/The-EKG-Sequence/em/1057777433.full">The EKG sequence</a>, Exper. Math. 11 (2002), 437-446; <a href="https://arxiv.org/abs/math/0204011">arXiv preprint</a>, arXiv:math/0204011 [math.NT], 2002.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EKGSequence.html">EKG Sequence</a>.
%H <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e Original permutation has cycles (1) (2) (3, 4, 6, 9, 10, 5) (..., 20, 18, 12, 7, 14, 13, 28, 26, ...) (8) ...
%t maxN=200; lst={1, 2}; unused=Range[3, maxN]; found=True; While[found, found=False; i=0; While[ !found&&i<Length[unused], i++; If[GCD[lst[[ -1]], unused[[i]]]>1, found=True; AppendTo[lst, unused[[i]]]; unused=Delete[unused, i]]]]; Take[Ordering[lst], unused[[1]]-1]
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a064664 = (+ 1) . fromJust . (`elemIndex` a064413_list)
%o -- _Reinhard Zumkeller_, May 01 2014, Sep 17 2011
%Y Cf. A064413, A064665, A064666, A064667, A064668, A064669.
%Y Equals A064421 + 1.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 11 2001
|
