A079300 - OEIS

%I #36 Nov 11 2021 20:10:27

%S 1,1,1,1,2,2,5,1,3,4,15,3,10,14,4,1,2,7,33,6,29,40,4,4,14,24,5,23,132,

%T 12,77,1,2,4,43,12,39,92,20,8,23,84,4,69,14,8,220,5,12,36,4,38,205,16,

%U 156,32,173,352,37,24,91,233,87,1,2,4,23,6,29,134,1258,18,49,104,32

%N a(n) = number of shortest addition chains ending in n.

%C An addition chain is a finite sequence of whole numbers starting with 1 in which each subsequent term is the sum of two (not necessarily distinct) earlier terms. - _Glen Whitney_, Nov 08 2021

%H Glen Whitney, <a href="/A079300/b079300.txt">Table of n, a(n) for n = 1..18286</a> (Terms 1..1024 from D. W. Wilson)

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/nsac_count_22.gz">Compressed table of a(n)</a> (for all n such that A003313(n) < 23, including all n < 196591)

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html">Shortest addition chains</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AdditionChain.html">Addition Chain</a>

%H Glen Whitney, <a href="/A079300/a079300.c.txt">C program to compute counts of addition chains</a>

%F a(n) = A079301(n) + A079302(n). - _Glen Whitney_, Nov 06 2021

%e 7 has a(7) = 5 shortest addition chains: (1,2,3,4,7), (1,2,3,5,7), (1,2,3,6,7), (1,2,4,5,7), (1,2,4,6,7).

%Y Cf. A003313, A118386, A118387.

%Y Cf. A079301, A079302, the number of shortest addition chains of Brauer and non-Brauer type, respectively.

%K nonn

%O 1,5

%A _David W. Wilson_, Feb 09 2003

%E More terms from _Don Reble_, Mar 31 2006

%E Name edited by _Glen Whitney_, Nov 08 2021