%I A117497
%S A117497 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,
%T A117497 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,
%U A117497 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 A117497 Length of shortest sequence b with b(0) = 1, b(i+1) = b(i)+d where d|b(i) 
               and b(k) = n.
%C A117497 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.
%F A117497 a(1)=0, a(n) = 1 + min_{d|n, d<n} a(n-d).
%e A117497 The sequence 1,2,4,8,16,32,64,128,132,143 gets 143 in 9 steps, so a(143) 
               = 9.
%Y A117497 Cf. A003313, A117498.
%Y A117497 Sequence in context: A128998 A137813 A003313 this_sequence A117498 A064097 
               A014701
%Y A117497 Adjacent sequences: A117494 A117495 A117496 this_sequence A117498 A117499 
               A117500
%K A117497 nonn
%O A117497 1,3
%A A117497 Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 22 2006