The first five heptagonal numbers [via Wikipedia]
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Geeky Maths Things: 148 – Heptagonal Numbers

Day 148 of my 365 project reminds me about heptagonal numbers.

148 is a good example of a heptagonal number because it fits two of the three heptagonal number categories: heptagonal numbers, centred heptagonal numbers and centred heptagonal primes.

The first five heptagonal numbers [via Wikipedia]
The first five heptagonal numbers [via Wikipedia]

As you can see, these numbers make heptagons. The first few heptagonal numbers are 1, 7, 18, 34, 55, 81, 112, 148… and are found using the formula frac{5n^{2}-3n}{2}.

Centred heptagonal numbers are similar, except the heptagons grow around a central point. 148 is the second number to be in both the sequence of heptagonal numbers and centred heptagonal numbers.

Centred heptagonal number sample (figurate numbers), 8, 22, 43, 71 points. [via Wikipedia]
Centred heptagonal number sample (figurate numbers), 8, 22, 43, 71 points. [via Wikipedia]
The first few centred heptagonal numbers are: 1, 8, 22, 43, 71, 106, 148… Centred heptagonal numbers are of the form frac{7n^{2}-7n+2}{2}.

 

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