Greatest prime dividing the n-th cubefree number: Difference between revisions
Greatest prime dividing the n-th cubefree number (view source)
Revision as of 08:07, 9 March 2024
, 3 months agojulia example
m (→resursive alternative: Using Apéry's Constant) |
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The 1000000th term of a[n] is 1202057
The 10000000th term of a[n] is 1202057</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Formatting
using Primes
using ResumableFunctions
const MAXINMASK = 10_000_000_000 # memory on test machine could not spare a bitmask much larger than this
""" return a bitmask containing at least max_wanted cubefreenumbers """
function cubefreemask(max_wanted)
size_wanted = Int(round(max_wanted * 1.21))
mask = trues(size_wanted)
p = primes(Int(floor(size_wanted^(1/3))))
for i in p
interval = i^3
for j in interval:interval:size_wanted
mask[j] = false
end
end
return mask
end
""" generator for cubefree numbers up to max_wanted in number """
@resumable function nextcubefree(max_wanted = MAXINMASK)
cfmask = cubefreemask(max_wanted)
@yield 1
for i in firstindex(cfmask)+1:lastindex(cfmask)
if cfmask[i]
@yield i
end
end
@warn "past end of allowable size of sequence A370833"
end
""" various task output with OEIS sequence A370833 """
function testA370833(toprint)
println("First 100 terms of a[n]:")
for (i, a) in enumerate(nextcubefree())
if i < 101
f = factor(a).pe # only factor the ones we want to print
highestprimefactor = isempty(f) ? 1 : f[end][begin]
print(rpad(highestprimefactor, 4), i % 10 == 0 ? "\n" : "")
elseif i ∈ toprint
highestprimefactor = (factor(a).pe)[end][begin]
println("\n The ", format(i, commas = true), "th term of a[n] is ",
format(highestprimefactor, commas = true))
end
i >= toprint[end] && break
end
end
testA370833(map(j -> 10^j, 3:Int(round(log10(MAXINMASK)))))
</syntaxhighlight>{{out}}
<pre>
First 100 terms of a[n]:
1 2 3 2 5 3 7 3 5 11
3 13 7 5 17 3 19 5 7 11
23 5 13 7 29 5 31 11 17 7
3 37 19 13 41 7 43 11 5 23
47 7 5 17 13 53 11 19 29 59
5 61 31 7 13 11 67 17 23 7
71 73 37 5 19 11 13 79 41 83
7 17 43 29 89 5 13 23 31 47
19 97 7 11 5 101 17 103 7 53
107 109 11 37 113 19 23 29 13 59
The 1,000th term of a[n] is 109
The 10,000th term of a[n] is 101
The 100,000th term of a[n] is 1,693
The 1,000,000th term of a[n] is 1,202,057
The 10,000,000th term of a[n] is 1,202,057
The 100,000,000th term of a[n] is 20,743
The 1,000,000,000th term of a[n] is 215,461
The 10,000,000,000th term of a[n] is 1,322,977
</pre>
=={{header|Pascal}}==
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