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%I #29 Jun 10 2024 23:22:13
%S 0,0,0,0,2,9,30,80,193,432,925,1928,3953,8024,16189,32544
%N Number of k in the range 2^n <= k < 2^(n+1) whose shortest addition chain does not have length n, n+1 or n+2.
%C The length of the shortest addition chain for k is A003313(k).
%C Dividing natural numbers into sections 2^n <= k < 2^(n+1), some of the 2^n numbers available in a section have the shortest addition chains given by
%C n (for k=2^n),
%C n+1 (for k=2^n+2^m, m in [0..n-1], A048645), or
%C n+2 (for some k in A072823).
%C The sequence gives the numbers of k within each section (N_oth) that have the shortest addition chains other than n, n+1, and n+2.
%C In particular for 4 <= n <= 6, N_oth = 2^n - n^2 + 2 and for n >= 7, N_oth = 2^n - n^2 + 1.
%H S. Łukaszyk and W. Bieniawski, <a href="https://doi.org/10.3390/math12101600">Assembly Theory of Binary Messages</a>, Mathematics, 12(10) (2024), 1600.
%Y Cf. A003313, A048645, A072823, A014701, A024012.
%K nonn,more
%O 0,5
%A _Szymon Lukaszyk_, Apr 20 2024