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Lexicographically earliest sequence of integers > 1 such that for any distinct m and n, a(m)^a(m+1) <> a(n)^a(n+1).
2

%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