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3

b) The shortest sequence is Method:


3

Answer to part c): Found with the following Python code: from heapq import heappush, heappop best_n = 0 candidates = [(1, [1], set((1,)))] while candidates: prev_max, prev_list, prev_set = heappop(candidates) n = len(prev_list) + 1 max_n = min(set(range(1, (n+1)+1)) - prev_set) - 1 if max_n > best_n: best_n = max_n ...


0

maybe 21 wasn't a mistake. 21,91,171,231,351,561,741 etcc are triangular numbers with cadence 1, obtained from the progressive arithmetic sum 1 + 2 + 3 + 4 + 5 + 6 ..... from the sequence it is clear that 21 is obtained from (6 + 1) * (6/2) and that the other numbers are obtained by the formula (x + 1 + k) * (x + k) /2 where x = 6 k=(+7,+5,+3,+5 ) repeted n ...


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