All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Consecutive Triangles (Posted on 2009-11-29) Difficulty: 4 of 5
A, B, C and D are triangular numbers.

A, B and C are always consecutive while D is their sum.

Determine (and explain as best as possible1) how such sets of values are distributed across the number system.

1. This can be explained in terms of a single variable expression.

See The Solution Submitted by brianjn    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: an observation | Comment 5 of 8 |
(In reply to an observation by Dej Mar)

Interesting, and valued.

I had derived that (3nē + 9n +8)/2 was the sum of 3 consecutive triangular numbers.  My issue was to determine a unit incremental value that would create that 'n'.

The formula offered, x = SQRT(3n2 + 9n + 33/4) - (1/2), equates to the Sloane sequence A082840 only when 'x' is an integer for unit increments of 'n'.

Edited on November 30, 2009, 7:18 pm
  Posted by brianjn on 2009-11-30 08:13:20

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information