Pell Number Evolution [ 80782 → 1000000 ] remix

Instructions

Evolve the number into a Pell number. Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + √2. As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combinatorial enumeration problems. The name of the Pell numbers stems from Leonhard Euler's mistaken attribution of the equation and the numbers derived from it to John Pell. The Pell numbers are defined by the recurrence relation: p(0) = 0, p(1) = 1, p(n) = 2 * p(n-1) + p(n-2) In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number and the Pell number before that. The first few terms of the sequence are: 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860,…