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=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: