Problems & Puzzles: Puzzles Puzzle 53. Sequences of consecutive economical numbers. A number E is called (after B. Recam) an economical number, if the expression of E as a product of powered primes uses fewer digits than the digits of E. The first 8 economical numbers are: 125, 128, 243, 256, 343, 512, 625, 729, …. (See Neils sequence A046759) 125 =5^3, 128 =2^7, etceteras. Do exist consecutive economical numbers? The answer is yes. Here we are interested only in the earliest sequences of K=>2 consecutive economical numbers. I have found the earliest sequences for K = 2, 3 and 4: K=2 K=3 K=4 (see also A047738) Q. Find the earliest sequence of 5<=K<=10 consecutive economical numbers.
Around ten years later, J. K. Andersen sent more solutions to this old but not dead and beloved puzzle of mine:
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