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 A117497 Length of shortest sequence b with b(0) = 1, b(i+1) = b(i)+d where d|b(i) and b(k) = n. 5
 0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 6, 6, 7, 6, 7, 7, 7, 6, 7, 7, 8, 7, 7, 8, 9, 6, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 9, 8, 8, 9, 9, 8, 9, 8, 9, 9, 9, 10, 9, 7, 8, 8, 8, 8, 9, 8, 9, 8, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is similar to the shortest addition chain for n. Both the binary method and the divisor method for finding an addition chain will find a sequence of this type. The smallest few n where there is an addition chain shorter than this sequence are 23,43,46,47,59. The first few n where this sequence is smaller than the shortest addition chain are 143,267,275,286,407. The smallest few n such that a(n) = a(2n) are 86,213,285,342,383. LINKS David W. Wilson, Table of n, a(n) for n = 1..10000 FORMULA a(1)=0, a(n) = 1 + min_{d|n, d

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Last modified January 27 15:02 EST 2022. Contains 350607 sequences. (Running on oeis4.)