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%I #23 Aug 04 2018 12:29:14
%S 1,4,4,4,6,6,12,8,10,10,10,18,14,14,14,24,16,20,22,22,22,27,30,25,35,
%T 28,26,26,26,36,32,34,34,34,42,38,38,38,45,40,44,46,46,46,48,50,52,54,
%U 56,49,63,60,55,65,70,58,58,58,66,62,62
%N The EKG sequence (A064413) smoothed by replacing each prime p with 2p and each thrice-prime 3p also with 2p.
%C This smoothing of A064413 is discussed in Lagarias et al. (2002).
%C a(n) = A256415(A064413(n)). - _Reinhard Zumkeller_, Apr 06 2015
%H Reinhard Zumkeller, <a href="/A256417/b256417.txt">Table of n, a(n) for n = 1..10000</a>
%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0204011">The EKG sequence</a>, arXiv:math/0204011 [math.NT], 2002.
%H 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.
%t ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
%t Nest[ekg, {1, 2}, 100] /. {n_ /; PrimeQ[n] -> 2n, n_ /; PrimeQ[n/3] -> 2n/3 } (* _Jean-François Alcover_, Aug 04 2018, after _Robert G. Wilson v_ *)
%o (Haskell)
%o a256417 = a256415 . a064413 -- _Reinhard Zumkeller_, Apr 06 2015
%Y Cf. A064413, A256415, A256416.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 05 2015
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