Squared digit sum. See https://twitter.com/AlgebraFact/status/977543329046056961 and https://www.johndcook.com/blog/2018/03/24/squared-digit-sum/

sqsum.rb

def sqsum(x)
  y = 0
  x.to_s.split(//).each do |s|
    a = s.to_i
    y += a ** 2
  end
  y
end

def seq_sqsum(x)
  h = {}
  while not h[x]
    print "#{x} -> "
    h[x] = true
    x = sqsum(x)
  end
  puts "#{x} -> ..."
end

seq_sqsum(4)
seq_sqsum(1000)
seq_sqsum(3)
seq_sqsum(31)
seq_sqsum(314)
seq_sqsum(3141)
seq_sqsum(31415)
seq_sqsum(314159)
seq_sqsum(3141592)
seq_sqsum(31415926)
seq_sqsum(314159265)

4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> ...
1000 -> 1 -> 1 -> ...
3 -> 9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> ...
31 -> 10 -> 1 -> 1 -> ...
314 -> 26 -> 40 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> ...
3141 -> 27 -> 53 -> 34 -> 25 -> 29 -> 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> ...
31415 -> 52 -> 29 -> 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> ...
314159 -> 133 -> 19 -> 82 -> 68 -> 100 -> 1 -> 1 -> ...
3141592 -> 137 -> 59 -> 106 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> ...
31415926 -> 173 -> 59 -> 106 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> ...
314159265 -> 198 -> 146 -> 53 -> 34 -> 25 -> 29 -> 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> ...

“任意の正整数から始め、その数を構成している各桁の数字を平方して足し合わせる操作を繰り返せ。すると必ず、1になって終わるか、8個の数をぐるぐる回るかのいずれかになる”
https://www.johndcook.com/blog/2018/03/24/squared-digit-sum/

def sqsum(x)
  x.to_s.split(//).map { |d| d.to_i ** 2 }.reduce(0) { |sum, sq| sum += sq }
end