World!Of
Numbers

WON plate
103 |

[ June 3, 2001 ]
Polygonals with palindromic sides, rank and number.
A list provided by Jeff Heleen (email)

Jeff borrowed the terminology from Albert H. Beiler's book
"Recreations in the Theory of Numbers", chapter XVIII.
Rank is just the number of the term (ie, 1st, 2nd, 3rd, etc.) for a particular polygon
(triangular, square, pentagonal, etc.) and number is just the result of using
the formula for that polygon with a given number of sides.
Example for a pentagon, sides = 5, formula is r(3r-1)/2, where r = rank.
So, the 4th pentagonal number (r = 4) is 22, which is palindromic.
I highlighted myself the entry with sides = 2002,
to inform that the last palindromic year of our lives is advancing...

Sides < 10001Rank < 101Number
336
439
5422
774454
1414838
1514898
79744774
7997447974
7555
555535
53555335
5335553335
6666
96111
116141
446636
42466336
4224663336
4554668286
38378008
646713531
119333
25299009
414914841
31166
411121
22111111
111116006
121116556
2021111011
200211110011
299211164461
422484
34333180081
70733372273
74733393393
111133585585
5442882
7444774
9446666
11448558
6555995
3773003
27277790097
22288842248
17199819918

The general formula for a n-gonal is r/2[(sides–2)r–(sides–4)]
Jeff Heleen re-discovered this list from his archive.
He cannot remember if the above list is exhaustive or not.
Can someone write a program to check out if the list is complete ?

[ Same day ]
Jeff rewrote the program from scratch and the output turned out
to be slightly longer than the original list. He believes the current list
is now closer to being exhaustive within the set ranges.

A000103 Prime Curios! Prime Puzzle
Wikipedia 103 Le nombre 103
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