```Here's my solution to find happy bases - note that I don't find any
happy bases (aside from 2 and 4) before I run out of memory, somewhere
near base 1700.  It wouldn't surprise me if no other happy bases
exist.

The program checks up to 2*(base-1)*(base-1) for numbers that fall
into an infinite loop (that is not '1' forever) when applying the
digit-square-sum function.  This is all that's needed, as it can
easily be shown that any number will eventually get less than that.

There's almost certainly some stuff I could do to be more parsimonious
with memory, chief among them finding a copy of narray that has the
.mod! method.  (I may revisit this and use a combination of div!, mul!
and sbt! to cut down on temporary arrays) However, this program as it
stands very quickly checks much farther out than I would have thought
necessary if there really were other happy bases out there to be
found.

#!/usr/bin/env ruby
require 'narray'

def dodigsum(base, initial)
tmp = initial / (base ** NArray.to_na([[0],[1],[2]]))
# I would use mod!, but my copy of narray doesn't have mod!
tmp = tmp % base
tmp.mul!(tmp)
end

def checkbase(base = 10)
base = base.to_i
checklimit = 2*(base-1)*(base-1)
check = NArray.int(checklimit + 1).indgen!
check_initial = check.dup

while true do
dodigsum(base,check)
if check.eq(check_initial).count_true > 2
#Gobs of debugging info
# puts "#{base} has a loop on #{lp}"
break
end
if check.le(1).count_true > checklimit
puts "#{base} is a happy base"
break
end
end
end

2.upto(3000) { |b|
begin
checkbase(b)
rescue Interrupt
puts "Checking #{b}"
checkbase(b)
rescue Error => e
puts "Bailing on #{b}"
raise e
end
}

__END__

--
s=%q(  Daniel Martin -- martin / snowplow.org
puts "s=%q(#{s})",s.map{|i|i}[1]       )
puts "s=%q(#{s})",s.map{|i|i}[1]

```