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%I #11 May 17 2020 06:21:29
%S 2,2,3,2,4,3,3,4,4,5,2,5,3,5,4,6,2,7,2,9,3,7,3,8,5,5,6,3,9,5,7,4,7,5,
%T 8,6,4,8,7,6,5,9,6,6,7,7,8,8,9,7,9,8,10,2,11,2,13,2,17,2,19,2,20,2,22,
%U 2,23,2,25,5,11,3,11,4,13,3,13,4,14,2,29,2
%N Lexicographically earliest sequence of integers > 1 such that for any distinct m and n, a(m)^a(m+1) <> a(n)^a(n+1).
%C This sequence has similarities with A088177; here we raise consecutive terms, there we multiply consecutive terms.
%C This sequence contains large runs of consecutive terms where every other term equals 2.
%H Rémy Sigrist, <a href="/A334857/b334857.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A334857/a334857.gp.txt">PARI program for A334857</a>
%e The first terms, alongside a(n)^a(n+1), are:
%e n a(n) a(n)^a(n+1)
%e -- ---- -----------
%e 1 2 4
%e 2 2 8
%e 3 3 9
%e 4 2 16
%e 5 4 64
%e 6 3 27
%e 7 3 81
%e 8 4 256
%e 9 4 1024
%e 10 5 25
%e 11 2 32
%e 12 5 125
%e 13 3 243
%o (PARI) See Links section.
%Y Cf. A088177, A334858.
%K nonn
%O 1,1
%A _Rémy Sigrist_, May 13 2020