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A251414 a(n) = (A251413(n) + 1)/2.

%I A251414 #28 Jan 29 2025 13:09:44
%S A251414 1,2,3,5,13,11,28,4,6,18,17,25,8,39,14,46,23,7,26,33,9,20,43,29,58,10,
%T A251414 12,48,35,63,32,73,41,15,38,102,47,60,16,53,171,44,61,56,72,19,50,93,
%U A251414 59,78,62,88,21,67,103,74,108,71,22,24,65,118,77,123,80,81
%N A251414 a(n) = (A251413(n) + 1)/2.
%C A251414 Conjectured to be a permutation of the natural numbers.
%D A251414 L. Edson Jeffery, Posting to Sequence Fans Mailing List, Dec 01 2014
%H A251414 N. J. A. Sloane, <a href="/A251414/b251414.txt">Table of n, a(n) for n = 1..11945</a>
%H A251414 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669, 2015.
%t A251414 max = 57; f = True; a = {1, 3, 5}; NN = Range[4, 1000]; s = 2*NN - 1; While[TrueQ[f], For[k = 1, k <= Length[s], k++, If[Length[a] < max, If[GCD[a[[-1]], s[[k]]] == 1 && GCD[a[[-2]], s[[k]]] > 1, a = Append[a, s[[k]]]; s = Delete[s, k]; k = 0; Break], f = False]]]; Table[(a[[n]] + 1)/2, {n, max}] (* _L. Edson Jeffery_, Dec 02 2014 *)
%o A251414 (Python)
%o A251414 from __future__ import division
%o A251414 from math import gcd
%o A251414 A251414_list, l1, l2, s, b = [1,2,3], 5, 3, 7, {}
%o A251414 for _ in range(1,10**2):
%o A251414     i = s
%o A251414     while True:
%o A251414         if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
%o A251414             A251414_list.append((i+1)//2)
%o A251414             l2, l1, b[i] = l1, i, True
%o A251414             while s in b:
%o A251414                 b.pop(s)
%o A251414                 s += 2
%o A251414             break
%o A251414         i += 2 # _Chai Wah Wu_, Dec 07 2014
%Y A251414 Cf. A098550, A251413.
%K A251414 nonn
%O A251414 1,2
%A A251414 _N. J. A. Sloane_, Dec 02 2014