[seqfan] Re: What are the possible digit-sums for Fibonacci numbers?
Hans Havermann
gladhobo at bell.net
Thu Dec 29 13:21:49 CET 2016
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).txt
0 {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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