PWC149 - Fibonacci Digit Sum


Here we are with TASK #1 from The Weekly Challenge #149. Enjoy!

The challenge

Given an input $N, generate the first $N numbers for which the sum of their digits is a Fibonacci number.


f(20)=[0, 1, 2, 3, 5, 8, 10, 11, 12, 14, 17, 20, 21, 23, 26, 30, 32, 35, 41, 44]

The questions

Well… this is nitpicking, I’ll read “numbers” as “positive integers”.

The solution

We’ll start with Raku:

#!/usr/bin/env raku
use v6;

class FibonacciSumming { ... }

sub MAIN ($N = 20) {
   my $fs =;
   $ for ^$N;

class FibonacciSumming {
   has %!fibo = 0 => 1;
   has $!f =  0;
   has $!s = -1;
   method next () {
      while True {
         my $sum = $!s.comb(/\d/).sum;
         ($!f, %!fibo{%!fibo{$!f}}) = %!fibo{$!f}, $!f + %!fibo{$!f}
            while $!f < $sum;
         return $!s if %!fibo{$sum}:exists;

We use an object to keep track of generating the outputs. There are three member variables:

  • %!fibo keeps track of the “following” number of Fibonacci numbers. I know that 1 has two successors, but it’s still working to indicate what is a Fibonacci number and what is not;
  • $!f is the companion to the hash above, keeping track of the latest key put in %!fibo, so that we can generate more;
  • $!s is a candidate result.

The main method next iterates until a suitable value is found in $!s. The $sum is calculated according to the rules, then it is checked against the Fibonacci numbers. The inner loop makes sure that there are enough Fibonacci numbers to check for presence of $sum

The Perl version is a sort of translation, only we’re opting for an iterator function here instead of a full-fledged object:

#!/usr/bin/env perl
use 5.024;
use warnings;
use English qw< -no_match_vars >;
use experimental qw< postderef signatures >;
no warnings qw< experimental::postderef experimental::signatures >;
use List::Util 'sum';

my $it = fibonacci_summing();
say $it->() for 1 .. (shift || 20);

sub fibonacci_summing {
   my %fibo = (0 => 1);
   my $f = 0;
   my $s = -1;
   return sub {
      while ('necessary') {
         my $sum = sum split m{}mxs, $s;
         ($f, $fibo{$fibo{$f}}) = ($fibo{$f}, $f + $fibo{$f})
            while $f < $sum;
         return $s if exists $fibo{$sum};

The returned sub closes over %fibo, $f, and $s, which have the same exact role as in the Raku version.

I guess this is all… until next time stay safe folks!

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