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Sequence of the Day

A182809: Fibonacci numbers that are base 10 cyclops numbers.

{0, 75025, 6557470319842, 14472334024676221, 99194853094755497, ... }
It’s not often that a basedependent 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 .

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On this day...

Sequences in the News
 Feb 01 2018 Alphabet announced a $8,589,869,056 = $A000396(6) stock buyback.
 Jan 03 2018 Largest known term of A000043 announced: 77232917.
 Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
 Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
 Jan 19 2016 Largest known term of A000043 announced: 74207281, also discovered by Curtis Cooper.
 Mar 02 2014 Fredrik Johansson announces a computation of the partition number p(10 20) ≈ 1.8381765 × 10 11140086259, the largest known term of A000041.
 Dec 06 2013 Microsoft launches a challenge to find large nonMersenne primes, A138837.


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