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%I
%S 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,
%T 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,
%U 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
%N Length of shortest sequence b with b(0) = 1, b(i+1) = b(i)+d where d|b(i) and b(k) = n.
%C 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.
%H <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%F a(1)=0, a(n) = 1 + min_{d|n, d<n} a(n-d).
%e The sequence 1,2,4,8,16,32,64,128,132,143 gets 143 in 9 steps, so a(143) = 9.
%Y Cf. A003313, A117498.
%K nonn
%O 1,3
%A _Franklin T. Adams-Watters_, Mar 22 2006
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