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special_form_carmichael.sf
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special_form_carmichael.sf
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#!/usr/bin/ruby
# Generate Carmichael numbers of special form.
func generate(a,b,c) {
var from = ((2**64 -> root(3) / (a*b*c).root(3) -> int))
from.is_even || ++from
from..Inf `by` 2 -> lazy.map {|m| (a*m + 1) * (b*m + 1) * (c*m + 1) }.grep { .is_carmichael }.first(100).each { .say }
}
DATA.each {|line|
if (line =~ /a,b,c\s*=\s*(\d+),(\d+),(\d+)/) {|m|
say ''
say line
generate(Num(m[0]), Num(m[1]), Num(m[2]))
}
}
__END__
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,53.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,55.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,61.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,67.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,19.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,23.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,39.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,51.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,57.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,63.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,65.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,69.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,5.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,7.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,9.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,11.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,13.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,15.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,17.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,21.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,25.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,27.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,29.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,31.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,37.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,41.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,43.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,45.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,47.
# N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,49.