%I A117498
%S A117498 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 A117498 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 A117498 9,7,8,8,8,8,9,8,9,7,8,8,9,8,8,9,9,8,9,8,9,9,9,10,9,7,8,8,8,8,9,8,9,8,
               9
%N A117498 Optimal combination of binary and factor methods for finding an addition 
               chain.
%C A117498 This is an upper bound for both addition chains (A003313) and A117497. 
               The first few values where A003313 is smaller are 23,43,46,47,59. 
               The first few values where A117497 is smaller are 77,143,154,172,
               173. The first few values where both are smaller are 77,154,172,173,
               203.
%F A117498 a(1)=0; a(n) = min(a(n-1)+1, min_{d|n, 1<d<n} a(d)+a(n/d)). If n is prime, 
               this reduces to a(n) = a(n-1)+1.
%e A117498 a(33)=6 because 6 = 1+a(32) < a(3)+a(11) = 2+5. a(36) = min(a(35)+1, 
               a(2)+a(18), a(3)+a(12), a(4)+a(9), a(6)+a(6)) = min(1+7, 1+5, 2+4, 
               2+4, 3+3) = 6.
%Y A117498 Cf. A003313, A117497, A064097.
%Y A117498 Sequence in context: A137813 A003313 A117497 this_sequence A064097 A014701 
               A056239
%Y A117498 Adjacent sequences: A117495 A117496 A117497 this_sequence A117499 A117500 
               A117501
%K A117498 nonn
%O A117498 1,3
%A A117498 Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 22 2006