This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 2
 1, 5, 13, 65, 97, 229, 997, 1145, 2245, 5725, 7213, 9805, 10445, 24193, 34121, 37321, 52225, 83729, 98449, 125233, 145493, 156925, 171037, 260893, 334981, 345725, 457813, 576757 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We have binary trees with the desired properties for every height n > 0: - for n = 1: we have the following tree B_1:                      1^2                       | - for any n > 0, provided we have B_n, we can build a tree B_{n+1) as follows:               3^2*B_n   4^2*B_n                   \       /                    \     /                     \   /                    (5^n)^2                       | - hence the sequence is well defined. LINKS Rémy Sigrist, Illustration of first terms Rémy Sigrist, C++ program for A309167 FORMULA a(n) <= 5^(n-1). A309228(a(n)) = n and A309228(k) < n for any k < a(n). EXAMPLE a(1) = 1:               1^2                | a(2) = 5:            3^2    4^2             \     /              \   /               5^2                | a(3) = 13:           3^2    4^2            \     /             \   /              5^2    12^2               \      /                \    /                 13^2                   | PROG (C++) See Links section. CROSSREFS Cf. A000351, A309228. Sequence in context: A149573 A149574 A301634 * A272069 A018678 A149575 Adjacent sequences:  A309164 A309165 A309166 * A309168 A309169 A309170 KEYWORD nonn,more AUTHOR Rémy Sigrist, Jul 15 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)