Template:Sequence of the Day for August 18

Intended for: August 18, 2011

Timetable

• First draft entered by Alonso del Arte on May 29, 2011 as a verbatim copy of the write-up from December 18, 2010 ✓
• Draft reviewed by Alonso del Arte on July 16, 2011 ✓
• Draft approved by Daniel Forgues on July 21, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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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

.