cielavenir

#!/usr/bin/ruby
t=[];p={};h={}
1.step(99999).map{|i|t.push(i*(i+1)/2);p[i*(3*i-1)/2]=1;h[i*(2*i-1)]=1}
p t.select{|e|p[e]&&h[e]}.drop(2).first #this select can be lazy

cielavenir

#!/usr/bin/ruby
require 'prime'
(9..1/0.0).each{|i|
	if i%2==0 || i.prime? then next end
	1.step(i){|j|
		if 2*j**2 > i then p i;exit end
		if (i-2*j**2).prime? then break end
	}
}

cielavenir

#!/usr/bin/ruby
require 'prime'
c=0;i=1
while c<4 do
	i+=1
	c=Prime.prime_division(i).count==4?c+1:0
end
p i-3

cielavenir

#!/usr/bin/ruby
p 1.step(1000).reduce(0){|s,i|s+=i**i}%10**10

cielavenir

#!/usr/bin/ruby
require 'prime'
h=Hash.new{|h,k|h[k]=[]}
Prime.each(9999).drop_while{|e|e<1000}.map{|e|h[e.to_s.split('').sort.join].push(e)}
h.each_value{|v|
	if v.length<3 then next end
	0.step(v.length-3){|i|
		(i+1).step(v.length-2){|j|
			(j+1).step(v.length-1){|k|
				if v[k]-v[j]==v[j]-v[i] then puts [v[i],v[j],v[k]].join end

cielavenir

#!/usr/bin/ruby
require 'prime'
a=Prime.each(100000).map{|e|e}
m=543
while true do
z=(a.length-m).times.map{|i|a[i,m].reduce(&:+)}.select{|e|e.prime?}[0]
if z then p z;exit end
m-=1
end

cielavenir

1/7.0 is 0.(142857), so the answer is 142857.

cielavenir

#!/usr/bin/ruby
class Integer
        def comb(r)
                if r==0 then return 1 end
                n=self
                ret=1
                if r>n/2 then r=n-r end
                r.times{|i|
                        ret=ret*(n-i)/(i+1)
                }

cielavenir

#!/usr/bin/ruby
p 1.step(99).map{|a|1.step(99).map{|b|(a**b).to_s.split('').map(&:to_i).reduce(&:+)}.max}.max

cielavenir

#!/usr/bin/ruby
q=[1,1];r=[0,1]
p 2.step(1001).select{|i|q.push(2*q[i-1]+q[i-2]);r.push(2*r[i-1]+r[i-2]);q[i].to_s.length>r[i].to_s.length}.count