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If ABC conjecture is true this sequence is finite.
a(4) is recent record of L(a,b,c) in general.
For numbers B for this case see A147641.
For numbers C for this case see A147642.
Function L(A,B,C) and A<B<C will be Log[C]/Log[rad[ABC]]
where function rad[ABC] is product of distinct prime divisors A*B*C and A,B,C don't have anyone that same prime divisor.
Successive records for L(A,B,C) see A147302.
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