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Metallic ratios: Difference between revisions

m
→‎{{header|REXX}}: made the output more aligned and consistent.
(→‎{{header|zkl}}: added code)
m (→‎{{header|REXX}}: made the output more aligned and consistent.)
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if words($)<n then $= subword($ copies('1 ', n), 1, n) /*extend list if too short*/
L= max(79108, length($) ) /*ensure width of title. */
say center(' Lucas sequence for the' !.m "ratio, where B is " m' ', L, "═")
say 'the first ' n " elements are:"
say $
say approx #-1 ' iterations with ' digs " decimal digits past the decimal point:"
say format(r,,digs); say
end /*m*/ /*stick a fork in it, we're all done. */</lang>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
════════════════════════════════════ Lucas sequence for the platinum ratio, where B is 0 ═════════════════════════════════════
the first 15 elements are:
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
the approximate value reached after 2 iterations with 32 decimal digits past the decimal point:
1.00000000000000000000000000000000
 
══════════════════════════════════════ Lucas sequence for the golden ratio, where B is 1 ═══════════════════════════════════════
the first 15 elements are:
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
the approximate value reached after 78 iterations with 32 decimal digits past the decimal point:
1.61803398874989484820458683436564
 
══════════════════════════════════════ Lucas sequence for the silver ratio, where B is 2 ═══════════════════════════════════════
the first 15 elements are:
1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243
the approximate value reached after 44 iterations with 32 decimal digits past the decimal point:
2.41421356237309504880168872420970
 
══════════════════════════════════════ Lucas sequence for the bronze ratio, where B is 3 ═══════════════════════════════════════
the first 15 elements are:
1 1 4 13 43 142 469 1549 5116 16897 55807 184318 608761 2010601 6640564
the approximate value reached after 34 iterations with 32 decimal digits past the decimal point:
3.30277563773199464655961063373525
 
══════════════════════════════════════ Lucas sequence for the copper ratio, where B is 4 ════════════════════════════════════════
the first 15 elements are:
1 1 5 21 89 377 1597 6765 28657 121393 514229 2178309 9227465 39088169 165580141
the approximate value reached after 28 iterations with 32 decimal digits past the decimal point:
4.23606797749978969640917366873128
 
══════════════════════════════════════════ Lucas sequence for the nickel ratio, where B is 5 ════════════════════════════════════════════
the first 15 elements are:
1 1 6 31 161 836 4341 22541 117046 607771 3155901 16387276 85092281 441848681 2294335686
the approximate value reached after 25 iterations with 32 decimal digits past the decimal point:
5.19258240356725201562535524577016
 
════════════════════════════════════════════ Lucas sequence for the aluminum ratio, where B is 6 ═════════════════════════════════════════════
the first 15 elements are:
1 1 7 43 265 1633 10063 62011 382129 2354785 14510839 89419819 551029753 3395598337 20924619775
the approximate value reached after 23 iterations with 32 decimal digits past the decimal point:
6.16227766016837933199889354443272
 
═══════════════════════════════════════════════════ Lucas sequence for the iron ratio, where B is 7 ════════════════════════════════════════════════════
the first 15 elements are:
1 1 8 57 407 2906 20749 148149 1057792 7552693 53926643 385039194 2749201001 19629446201 140155324408
the approximate value reached after 22 iterations with 32 decimal digits past the decimal point:
7.14005494464025913554865124576352
 
══════════════════════════════════════════════════════ Lucas sequence for the tin ratio, where B is 8 ═══════════════════════════════════════════════════════
the first 15 elements are:
1 1 9 73 593 4817 39129 317849 2581921 20973217 170367657 1383914473 11241683441 91317382001 741780739449
the approximate value reached after 20 iterations with 32 decimal digits past the decimal point:
8.12310562561766054982140985597408
 
Line 302:
the first 15 elements are:
1 1 10 91 829 7552 68797 626725 5709322 52010623 473804929 4316254984 39320099785 358197153049 3263094477226
the approximate value reached after 20 iterations with 32 decimal digits past the decimal point:
9.10977222864644365500113714088140
</pre>
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