This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309167 #29 Dec 09 2024 17:28:20
%S A309167 1,5,13,65,97,229,997,1145,2245,5725,7213,9805,10445,24193,34121,
%T A309167 37321,52225,83729,98449,125233,145493,156925,171037,260893,334981,
%U A309167 345725,457813,576757,755173,806885,839285,924157
%N A309167 a(n)^2 is the least possible value at the root of a binary tree of height n where all nodes hold positive squares and all interior nodes also equal the sum of their two children.
%C A309167 We have binary trees with the desired properties for every height n > 0:
%C A309167 - for n = 1: we have the following tree B_1:
%C A309167 1^2
%C A309167 |
%C A309167 - for any n > 0, provided we have B_n, we can build a tree B_{n+1} as follows:
%C A309167 3^2*B_n 4^2*B_n
%C A309167 \ /
%C A309167 \ /
%C A309167 \ /
%C A309167 (5^n)^2
%C A309167 |
%C A309167 - hence the sequence is well defined.
%H A309167 Rémy Sigrist, <a href="/A309167/a309167.png">Illustration of first terms</a>
%H A309167 Rémy Sigrist, <a href="/A309167/a309167_1.txt">C++ program for A309167</a>
%F A309167 a(n) <= 5^(n-1).
%F A309167 A309228(a(n)) = n and A309228(k) < n for any k < a(n).
%e A309167 a(1) = 1:
%e A309167 1^2
%e A309167 |
%e A309167 a(2) = 5:
%e A309167 3^2 4^2
%e A309167 \ /
%e A309167 \ /
%e A309167 5^2
%e A309167 |
%e A309167 a(3) = 13:
%e A309167 3^2 4^2
%e A309167 \ /
%e A309167 \ /
%e A309167 5^2 12^2
%e A309167 \ /
%e A309167 \ /
%e A309167 13^2
%e A309167 |
%o A309167 (C++) See Links section.
%Y A309167 Cf. A000351, A309228.
%K A309167 nonn,more
%O A309167 1,2
%A A309167 _Rémy Sigrist_, Jul 15 2019
%E A309167 a(29)-a(32) from _Rémy Sigrist_, Nov 16 2020