N this problem we consider sum-sequences of numbers; that is, sequences that start with 1, and where each number that comes later in the sum-sequence is the sum of two previous numbers, including the possibility of adding a number to itself. For example, 1, 2, 4, 8, 16 is a sum-sequence, where each number is adding the previous number to itself. Also, 1, 2, 3, 5, 8, 13 is a sum-sequence, where after adding 1 to itself, each number is the sum of the two previous. The following is also a sum-sequence: 1, 2, 3, 4, 5, 6, obtained by adding 1 to the previous number to get the next. More formally, let a -sum-sequence be a sequence of integers 1, 2, … , , such that 1 = 1 and for = 2, … , , there are , such that. ≤ < . and = + . For each positive integer we can look for the smallest such that there is a -sum sequence ending in . For example, we can get = 10, from the sequence 1, 2, 4, 8, 10, with = 5. a) Show that we cannot get = 10, with a sequence where < 5. b) The method above used to get = 10 with = 5 was to add the previous number to itself until it was the largest power of 2 less-than-or-equal-to , and then add the smaller powers of 2 together to get . For example, we can get 13 from the sequence 1, 2, 4, 8, 12 = 8 + 4, 13 = 12 + 1. We call this the double first method. Find an upper bound on the size of in terms of using the double-first method.