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%I #36 Jul 22 2018 08:49:07
%S 1,2,6,3,12,4,8,24,120,30,10,5,15,60,20,40,280,56,14,7,21,42,168,84,
%T 28,140,35,70,210,105,420,840,7560,1080,216,54,18,9,27,108,36,72,360,
%U 90,45,135,270,1890,378,126,63,189,756,252,504,1512,16632,1848,264
%N Lexicographically earliest sequence of distinct positive terms such that the Fermi-Dirac factorizations of two consecutive terms differ by exactly one factor.
%C For Fermi-Dirac representation of n see A182979. - _N. J. A. Sloane_, Jul 21 2018
%C For any n > 0, either a(n)/a(n+1) or a(n+1)/a(n) belongs to A050376.
%C This sequence has similarities with A282291; in both sequences, each pair of consecutive terms contains a term that divides the other.
%H Rémy Sigrist, <a href="/A298480/b298480.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A298480/a298480.gp.txt">PARI program for A298480</a>
%F A000120(A052331(a(n)) XOR A052331(a(n+1))) = 1 for any n > 0 (where XOR denotes the bitwise XOR operator).
%F Apparently, a(n) = A052330(A163252(n-1)) for any n > 0.
%e The first terms, alongside a(n+1)/a(n), are:
%e n a(n) a(n+1)/a(n)
%e -- ---- -----------
%e 1 1 2
%e 2 2 3
%e 3 6 1/2
%e 4 3 2^2
%e 5 12 1/3
%e 6 4 2
%e 7 8 3
%e 8 24 5
%e 9 120 1/2^2
%e 10 30 1/3
%e 11 10 1/2
%e 12 5 3
%e 13 15 2^2
%e 14 60 1/3
%e 15 20 2
%e 16 40 7
%e 17 280 1/5
%e 18 56 1/2^2
%e 19 14 1/2
%e 20 7 3
%o (PARI) See Links section.
%Y Cf. A000120, A050376, A052330, A052331, A282291, A182979.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Jul 21 2018