Smallest number k such that k+2^m is composite for all m less than k: Difference between revisions
→{{header|Wren}}: Slightly more efficient. |
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=={{header|Phix}}== |
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<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> |
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> |
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<span style="color: #008080;">function</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> |
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<span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">return</span> <span style="color: #004600;">true</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">5</span> <span style="color: #008080;">do</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> |
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> |
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> |
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<!--</lang>--> |
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{{out}} |
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Rather slow, even worse under pwa/p2js - about 90s... |
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<pre> |
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773 2131 2491 4471 5101 |
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"22.7s" |
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</pre> |
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=={{header|Raku}}== |
=={{header|Raku}}== |
Revision as of 18:32, 12 January 2022
Generate the sequence of numbers a(k), where each k is the smallest positive integer such that k + 2m is composite for every positive integer m less than k.
- For example
Suppose k == 7; test m == 1 through m == 6. If any are prime, the test fails.
Is 7 + 21 (9) prime? False
Is 7 + 22 (11) prime? True
So 7 is not an element of this sequence.
It is only necessary to test odd natural numbers k. An even number, plus any positive integer power of 2 is always composite.
- Task
Find and display, here on this page, the first 5 elements of this sequence.
- See also
OEIS:A033939 - Odd k for which k+2^m is composite for all m < k
Phix
with javascript_semantics atom t0 = time() include mpfr.e mpz z = mpz_init() function a(integer k) if k=1 then return false end if for m=1 to k-1 do mpz_ui_pow_ui(z,2,m) mpz_add_si(z,z,k) if mpz_prime(z) then return false end if end for return true end function integer k = 1, count = 0 while count<5 do if a(k) then printf(1,"%d ",k) count += 1 end if k += 2 end while printf(1,"\n") ?elapsed(time()-t0)
- Output:
Rather slow, even worse under pwa/p2js - about 90s...
773 2131 2491 4471 5101 "22.7s"
Raku
<lang perl6>put (1..∞).hyper(:250batch).map(* × 2 + 1).grep( -> $k { !(1 ..^ $k).first: ($k + 1 +< *).is-prime } )[^5]</lang>
- Output:
773 2131 2491 4471 5101
Wren
An embedded version as, judging by the size of numbers involved, Wren-CLI (using BigInt) will be too slow for this.
Brute force approach - takes a smidge under 2 seconds. <lang ecmascript>import "./gmp" for Mpz
// returns true if k is a sequence member, false otherwise var a = Fn.new { |k|
if (k == 1) return false for (m in 1...k) { var n = Mpz.one.lsh(m).add(k) if (n.probPrime(15) > 0) return false } return true
}
var count = 0 var k = 1 while (count < 5) {
if (a.call(k)) { System.write("%(k) ") count = count + 1 } k = k + 2
} System.print()</lang>
- Output:
773 2131 2491 4471 5101