Happy number

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A number is a happy number when the sum of the squares of its digits eventually becomes 1. Numbers that are not happy are called unhappy numbers.

Consider a number t, then define a sequence t0,t1,t2,.. where t0 = t, and ti+1 is the sum of the squares of the digits of ti. t is said to be happy if and only if this sequence is eventually 1, that is for some i, ti = 1.

Thus 7 is happy, as the associated sequence is:

(72) = 49
(42 + 92) = 97
(92 + 72) = 130
(12 + 32) = 10
(12) = 1

A number t is (un)happy iff all members of the above sequence are (un)happy.

The first 20 happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100.


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