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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

The first triangular number is 1.

To continue this thread, simply

add 2, then 3, then 4, on forever

to make triangular numbers.

So I'll go first:

**1**

(one)

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

3 is triangular and prime.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**G-man****Member**- Registered: 2011-02-28
- Posts: 16

6 Its triangular & first composite which isn't a square.

Maths!......

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

10 - The number of balls in a 10 ball rack. The first 2 digit triangular number! Also it is larger than 1 - 9 and has a zero in it.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

15

5 x (6/2)

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

21 everybody's favorite number

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

28: has factors 1, 2, 4, 7, 14, 28 and reminds me of February

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**G-man****Member**- Registered: 2011-02-28
- Posts: 16

36

square of product of first two consecutive primes.

Maths!......

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

45 - ( Colt ) the best automatic ever made.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**G-man****Member**- Registered: 2011-02-28
- Posts: 16

55..........

Maths!......

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

66 - the 11 the triangular number and the name of a now infamous highway here in the southwest.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**matthen****Member**- Registered: 2011-03-06
- Posts: 8

78

note these triangular numbers go:

...,**4**5,5**5**,6**6**,**78,9**1, quite cool that 4,5,6,7,8,9 appear in order with no interruptions!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

91 The most powerful triangular number and the one that wants to be a square the most. Also it is the only one that is 7 * 13.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

105=14+91

(14/2)*15

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

The 15th triangular number is 120. Which is also 5!.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**G-man****Member**- Registered: 2011-02-28
- Posts: 16

136.........1, 3 & 6 are first 3 triangle numbers.

Maths!......

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

153

Is a square away from 2 squares. 12^2 + 3^3 = 153 and 13^2 - 4^2 = 153

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

171

153 + 18 = 171

(19 x 18) / 2

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

210

210 = 190 + 20

210 = 14 x 15 = (21 x 20) / 2 on this post # 20.

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

231

One of the permutations of 123.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

253

253 = 231 + 22 = (1 + 22)+(2 + 21)+...(9 + 14)+(10 + 13)+(11 + 12)

= 11 x 23 = (23 x 22) / 2

This triangular number can form a digital triangle with 22 rows in 3 angles differing by 120 degrees.

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

276

And that is real close to 253.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

300

Yeah 300!!!! 276 + 24. (25 x 24) / 2 A triangle with 24 rows.

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,616

325 which is 3*5 - 2 = 13.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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