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A376449 Smallest sum of addition chain for n.

%I A376449 #21 Apr 22 2025 17:21:02
%S A376449 0,1,3,3,6,6,10,7,12,11,17,12,19,17,21,15,24,21,29,21,31,28,34,24,36,
%T A376449 32,39,31,46,36,48,31,48,41,52,39,56,48,58,41,62,52,64,50,66,57,74,48,
%U A376449 73,61,75,58,82,66,83,59,86,75,90,66,93,79,94,63,96,81,101,75,103,87,112,75,112,93,111
%N A376449 Smallest sum of addition chain for n.
%C A376449 There are multiple ways to get a shortest addition chain (A003313), this sequence is the smallest sum of the possible chains.
%H A376449 Roy van Rijn, <a href="/A376449/b376449.txt">Table of n, a(n) for n = 1..100</a>
%F A376449 For n = 2^s, a(n) = n-1.
%F A376449 For odd n, a(n) = A008057((n-1)/2) - n + 1. - _Pontus von Brömssen_, Apr 22 2025
%e A376449 Here are the smallest examples:
%e A376449    n : a(n)
%e A376449    1 :  0    []
%e A376449    2 :  1    [1]
%e A376449    3 :  3    [1, 2]
%e A376449    4 :  3    [1, 2]
%e A376449    5 :  6    [1, 2, 3]
%e A376449    6 :  6    [1, 2, 3]
%e A376449    7 : 10    [1, 2, 3, 4]
%e A376449    8 :  7    [1, 2, 4]
%e A376449    9 : 12    [1, 2, 4, 5]
%e A376449   10 : 11    [1, 2, 3, 5]
%e A376449   11 : 17    [1, 2, 3, 5, 6]
%e A376449   12 : 12    [1, 2, 3, 6]
%e A376449   13 : 19    [1, 2, 3, 6, 7]
%e A376449   14 : 17    [1, 2, 3, 4, 7]
%e A376449   15 : 21    [1, 2, 3, 6, 9]
%e A376449   16 : 15    [1, 2, 4, 8]
%e A376449   17 : 24    [1, 2, 4, 8, 9]
%e A376449   18 : 21    [1, 2, 4, 5, 9]
%e A376449   19 : 29    [1, 2, 3, 4, 8, 11]
%e A376449   20 : 21    [1, 2, 3, 5, 10]
%e A376449   ...
%Y A376449 Cf. A003313, A008057.
%K A376449 nonn
%O A376449 1,3
%A A376449 _Roy van Rijn_, Sep 23 2024