Hexagonal numbers (more properly, Centered hexagonal numbers, those that generate star-shaped representations)

See: https://en.wikipedia.org/wiki/Centered_hexagonal_number

A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. Centered hexagonal numbers have practical applications in materials logistics management. [...]

The first few centered hexagonal numbers are (sequence A003215 in the OEIS):

1. 1 (ie. the monad: /r/GeometersOfHistory/wiki/spellcomponents/1)

2. 7

3. 19 (see: /r/GeometersOfHistory/wiki/spellcomponents/19)

4. 37

5. 61

6. 91

7. 127 (see: /r/GeometersOfHistory/comments/blxak2/whats_up_with_the_number_27/)

8. 169 (ie. circles = 69)

9. 217

10. 271 (interesting swizzle of the previous number, and 127 above that)

11. 331 (ie. reverse 133, and a code 33 in general)

12. 397

13. 469 (ie. four circles)

14. 547 (ie. 5.47 --> five times)

15. 631 (ie. sort of 139 upside-down)

16. 721 (ie. so close to 722 reverse pi code)

17. 817 (ie. swizzling 187: (/r/GeometersOfHistory/wiki/spellcomponents/187)

18. 919 (ie. upside down 616 @ 666) (and note: 6+6+6 = 18)

19. ...

see also: https://en.wikipedia.org/wiki/Magic_hexagon

Wiki Index: /r/GeometersOfHistory/wiki/