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Sequence of the Day for August 18

A182809: Fibonacci numbers that are base 10 cyclops numbers.

{0, 75025, 6557470319842, 14472334024676221, 99194853094755497, ... }

It’s not often that a base-dependent integer sequence (Keyword: base) piques my interest. When I first saw it, my first thoughts were “Keywords: Base and hard and more? We’ll see about that.” I thought a quick and dirty Mathematica program would prove that more terms are easy to come by and the keywords hard and more are totally unwarranted.

Well, I was wrong. Indeed, a little reflection and commonsense will show that the likelihood that Fibonacci numbers with more and more digits will have only one instance of the digit 0, and that that digit will be precisely in the middle, is increasingly improbable. And yet, commonsense is insufficient to prove with mathematical certainty that this sequence is finite and given in full. The most that we can say for now is that there are no more terms less than
F10 7

The following is in the <noinclude> ... </noinclude> section.

For more details about today's Sequence of the Day, see {{Sequence of the Day for August 18}}.

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