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Neal Gersh Tolunsky, <a href="/A366691/b366691_2.txt">Table of n, a(n) for n = 1..10000</a>
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Neal Gersh Tolunsky, <a href="/A366691/b366691_2.txt">Table of n, a(n) for n = 1..10000</a>
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Two consecutive values enclose 0 terms, and thus after {[a(1), a(2)} ] = {[1, 1}, ], no consecutive equal values occur again.
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Note that we are considering sets between every pair of equal values, not just those that appear consecutively.
a(2)=1 creates the pair {[1, 1}, ], which encloses 0 elements. This means that no consecutive equal values can occur again, since this would create another set of 0 elements.
a(4)=1 creates two new sets {: [1, 2, 1}, ], enclosing 1 element {2}, and {[1, 1, 2, 1}, ], enclosing 2 elements {1, 2}.
a(5) cannot be 1 as this would again create a pair enclosing 0 elements {[1,1}]. 2 would create the set {pair [2, 1, 2} ] which encloses 1 element {1}, which has been impossible since a(4). So a(5)=3, which has not occurred before.
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Neal Gersh Tolunsky, <a href="/A366691/b366691_2.txt">Table of n, a(n) for n = 1..10000</a>
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