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 Consecutive Triangles (Posted on 2009-11-29)
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

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 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

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