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%I #27 Sep 04 2018 09:18:26
%S 1,2,3,5,6,15,17,33,41,55,57,65,70,105,129,257,273,385,561,897,969,
%T 1001,1105,1353,1430,1785,2049,2145,2337,2665,3553,4097,4305,4745,
%U 4845,5633,6105,6545,8193,8385
%N A222311 sorted and duplicates removed (conjectured).
%C Obtained by sorting and removing duplicates from the first 500 terms of A222311. There is no proof as yet that this list is complete up to 105. Only the first three terms shown are certain. Is there a proof that 4 cannot appear?
%H Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, <a href="http://arxiv.org/abs/1511.04315">A growth model based on the arithmetic Z-game</a>, arXiv:1511.04315 [math.NT], 2015.
%H Cristian Cobeli, Alexandru Zaharescu, <a href="http://arxiv.org/abs/1411.1334">A game with divisors and absolute differences of exponents</a>, arXiv:1411.1334 [math.NT], 2014 (see page 12).
%t terms = 40; nmax0 = 5000;
%t seq[nmax_] := seq[nmax] = Union[Print[nmax]; Join[r = {1}, Table[Reverse[r = FoldList[#1*(#2/GCD[#1, #2]^2) & , n, r]], {n, 2, nmax}][[All, 1]]]][[1 ;; terms]];
%t seq[nmax = nmax0]; seq[nmax = 2 nmax]; While[seq[nmax] == seq[nmax/2], nmax = 2 nmax]; seq[nmax] (* _Jean-François Alcover_, Sep 04 2018, after _Ivan Neretin_ in A222310 *)
%Y Cf. A222310, A222311.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Feb 16 2013
%E Corrected and extended using data from Cobeli et al., 2015. - _N. J. A. Sloane_, Aug 27 2016
%E More terms (computed from a list of 10000) from _Jean-François Alcover_, Sep 04 2018
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