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Palindromic Nonagonals (or 9-gonals) (or enneagonal)
Factorization Records triangle square penta hexa hepta octa

  left to right (forwards) as from the right to left (backwards)

Nonagonal numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
So, this line is for experts only

base x ( 7 x base - 5 ) ------------------------------- 2

So far this compilation counts 65 Palindromic Nonagonals.

A palindromic nonagonal numbers can only end with digit 0, 1, 4, 5, 6, and 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.

There exist no palindromic nonagonals of length

A B C →  14 9 1 

A B C →  14 23 9 

Sloane's A048909 gives the first numbers that are both Nonagonal and Triangular.

Sloane's A036411 gives the first numbers that are both Nonagonal and Square.

Sloane's A048915 gives the first numbers that are both Nonagonal and Pentagonal.

Sloane's A048918 gives the first numbers that are both Nonagonal and Hexagonal.

Sloane's A048921 gives the first numbers that are both Nonagonal and Heptagonal.

Sloane's A048924 gives the first numbers that are both Nonagonal and Octagonal.

The best way to get a 'structural' insight as how to imagine nonagonals is to visit for instance this site :

• From Eric Weisstein's Math Encyclopedia : Nonagonal Number

Neil Sloane's “Integer Sequences” Encyclopedia can be consulted online : Neil Sloane's Integer Sequences One can find the regular nonagonal numbers at %N 9-gonal (or enneagonal or nonagonal) numbers: n(7n–5)/2 under A001106. The palindromic nonagonal numbers are categorised as follows : %N n(7n–5)/2 is a palindromic nonagonal number under A055560. %N Palindromic nonagonal numbers under A082723. Click here to view some of the author's [P. De Geest] entries to the table. Click here to view some entries to the table about palindromes.

Feng Yuan (email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number [1] up to [44].

[ January 8, 2008 ]
Feng Yuan (email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number [45] up to [52].

Higher values up to length 47 were found and submitted by Feng Yuan.

Exhaustive (re)-search performed up to length 36 by Patrick De Geest and found no missers.

[ November 4, 2022 ]
Robert Xiao (email) added four missing entries [46], [47], [49] and [53].

[ November 11, 2022 ]
Robert Xiao (email) added two missing entries [56] and [57].

[ November 13, 2022 ]
David Griffeath (email) using Rust code by Robert Xiao (email) discovered a record entry [60].

[ December 6, 2022 ]
Robert Xiao (email) added one missing entry [58].

[ January 11, 2023 ]
David Griffeath (email) using CUDA code by Robert Xiao (email) did a search for 53-digit palindromic nonagonals but there are none.
So he pushed through to 54 digits and found two new record entries [61] and [62], one with even root and one with odd root.

[ June 16, 2023 ]
Patrick De Geest (email) using CUDApalin from R. Xiao added three more entries [63] up to [65].

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( © All rights reserved ) - Last modified : July 3, 2023.

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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com

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