[seqfan] Re: What are the possible digit-sums for Fibonacci numbers?

Frank Adams-Watters franktaw at netscape.net
Thu Dec 29 15:17:36 CET 2016


Probabilistically, one would expect there to be infinitely many such. From the b-file, it appears that 44 and 45 are the first two.

Franklin T. Adams-Watters


-----Original Message-----
From: Hans Havermann <gladhobo at bell.net>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Thu, Dec 29, 2016 6:21 am
Subject: [seqfan] Re: What are the possible digit-sums for Fibonacci numbers?

I've put up a million-line, base-ten, Fibonacci-digits sums cheat sheet (~18 MB, give it some time to fully load) so that one may better appreciate the expected "normality" of large decimal Fibonacci numbers:

http://chesswanks.com/num/FibonacciDigitsSums(b10).txt0 {0}1 {1,2}2 {3}3 {4,8}4 {7}5 {5}6 {}7 {9,15}...2016 {}2017 {2161,2202} (happy upcoming new year!)2018 {2019}2019 {}...
The sums are on the left and the bracketed "solutions" are the Fibonacci indices whose Fibonacci decimal expansions result in those sums. 
It isn't just empty lists that are expected to be final (with no further solutions) but all lists. One will better see why A020995 should be both finite and full. 
I'm working on a base-two version of the cheat sheet where the sums are closer together. 

Before working it out, take a guess: Are there nonnegative integers in A011373 that will never appear?

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