Talk:Centered polygonal number

Karl, it's very nice to have this article. But the changes you made to the linked articles seemed very wrong to me for some reason:

A centered k-agonal number is a figurate number that represents a k-agon ...

So I changed them to

A centered k-agonal number is a centered figurate number that represents a k-agon ...

Anton Mravcek 21:13, 27 Jul 2004 (UTC)

Anton, I agree with your changes. Further thought, suggests that Centred number should be moved to Centred polygonal number like Polygonal number.

User:Karl Palmen 12:15 28 Jul 2004 (UTC)

• Oppose. I think it's a terrible idea, especially for centered hexagonal numbers. For the others, a case can be made, but still not likely to convince me. PrimeFan 21:38, 15 March 2007 (UTC) [reply ]

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"The difference of the n-th and the (n+1)-th consecutive centered k-gonal numbers is k(2n+1)." Is unclear. When I solve the the difference between (n+1)-th centered k-gonal number and n-th centered k-gonal number I get k(2n). More generally, if you solve for difference of (n+p)-th centered k-gonal number and n-th k-gonal number you get ${\displaystyle C_{k,n+p}-C_{k,n}={\frac {kp}{2}}(2n+p-1)}${\displaystyle C_{k,n+p}-C_{k,n}={\frac {kp}{2}}(2n+p-1)}. Returning to ${\displaystyle k(2n+1)}${\displaystyle k(2n+1)}, I'm assuming you can simply say that ${\displaystyle k={\frac {kp}{2}}}${\displaystyle k={\frac {kp}{2}}} and ${\displaystyle 1=p-1}${\displaystyle 1=p-1}, which is satisfied by p=2, not p=1. Is the original phrase supposed to mean the difference in ${\displaystyle C_{k,n+1}-C_{k,n}}${\displaystyle C_{k,n+1}-C_{k,n}} or something else entirely? Hiruki8 (talk) 22:07, 12 January 2024 (UTC) [reply ]

If the given polygon contains even number of sides, then the numbers are all odd. If the given polygon contains odd number of sides, then the numbers alternate between two odd and two even, starting with 0th centred polygonal number (1). Usermaths (talk) 15:15, 8 November 2024 (UTC) [reply ]

Please read WP:OR. Wikipedia articles and talk-pages are not an appropriate place to conduct or promote your own individual research into parities of numerical sequences. 100.36.106.199 (talk) 17:40, 8 November 2024 (UTC) [reply ]

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