Metallic ratios: Difference between revisions
→{{header|Perl 6}}: Rewrote more modular, always show trailing zeros, add stretch goal
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=={{header|Perl 6}}==
{{works with|Rakudo|2019.07.1}}
Note: Arrays, Lists and Sequences are zero indexed in Perl 6.
<lang perl6>use Rat::Precise;
use Lingua::EN::Numbers;
sub lucas ($b) { 1, 1, * + $b * * … * }
for <Platinum Golden Silver Bronze Copper Nickel Aluminum Iron Tin Lead>.kv▼
-> \b, $name {▼
sub metallic ($seq, $places = 32) {
print "\nLucas sequence for $name ratio; where b = {b}:\nFirst 15 elements: ";▼
my $
say join ', ', $L[^15];▼
my $N = 0;▼
my $last = 0;
loop {
my $approx = FatRat.new($
my $this = $approx.precise($places, :z);
last if $this eq $last;
$last = $this;
$
}
$last, $n
say "Approximated value: $last - Reached after {$N} iterations: " ~▼
}
"{ordinal-digit $N}/{ordinal-digit $N - 1} element. (zero indexed)";▼
sub display ($value, $n) {
}
▲for <Platinum Golden Silver Bronze Copper Nickel Aluminum Iron Tin Lead>.kv
▲ -> \b, $name {
▲ print "\nLucas sequence for $name ratio; where b = {b}:\nFirst 15 elements: ";
say join ' ', display |metallic($lucas);
}
# Stretch goal
say "\nGolden ratio to 256 decimal places:\n" ~ join "\n", display |metallic lucas(1), 256;</lang>
{{out}}
<pre>Lucas sequence for Platinum ratio; where b = 0:
First 15 elements: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Approximated value: 1.
Lucas sequence for Golden ratio; where b = 1:
First 15 elements: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
Approximated value: 1.61803398874989484820458683436564
Lucas sequence for Silver ratio; where b = 2:
First 15 elements: 1, 1, 3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119, 19601, 47321, 114243
Approximated value: 2.41421356237309504880168872420970
Lucas sequence for Bronze ratio; where b = 3:
First 15 elements: 1, 1, 4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564
Approximated value: 3.30277563773199464655961063373525
Lucas sequence for Copper ratio; where b = 4:
First 15 elements: 1, 1, 5, 21, 89, 377, 1597, 6765, 28657, 121393, 514229, 2178309, 9227465, 39088169, 165580141
Approximated value: 4.23606797749978969640917366873128
Lucas sequence for Nickel ratio; where b = 5:
First 15 elements: 1, 1, 6, 31, 161, 836, 4341, 22541, 117046, 607771, 3155901, 16387276, 85092281, 441848681, 2294335686
Approximated value: 5.19258240356725201562535524577016
Lucas sequence for Aluminum ratio; where b = 6:
First 15 elements: 1, 1, 7, 43, 265, 1633, 10063, 62011, 382129, 2354785, 14510839, 89419819, 551029753, 3395598337, 20924619775
Approximated value: 6.16227766016837933199889354443272
Lucas sequence for Iron ratio; where b = 7:
First 15 elements: 1, 1, 8, 57, 407, 2906, 20749, 148149, 1057792, 7552693, 53926643, 385039194, 2749201001, 19629446201, 140155324408
Approximated value: 7.14005494464025913554865124576352
Lucas sequence for Tin ratio; where b = 8:
First 15 elements: 1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449
Approximated value: 8.12310562561766054982140985597408
Lucas sequence for Lead ratio; where b = 9:
First 15 elements: 1, 1, 10, 91, 829, 7552, 68797, 626725, 5709322, 52010623, 473804929, 4316254984, 39320099785, 358197153049, 3263094477226
Approximated value: 9.10977222864644365500113714088140
Golden ratio to 256 decimal places:
Approximated value:
1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144
Reached after 615 iterations: 615th/614th element.</pre>
=={{header|REXX}}==
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