World!Of
Numbers
HOME plate
WON |

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



Introduction

Palindromic numbers are numbers which read the same from

 p_right left to right (forwards) as from the right to left (backwards) p_left
Here are a few random examples : 7, 3113, 44611644

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


Normal and Palindromic Nonagonals

flash So far I compiled 51 Palindromic Nonagonals.

These were all found by Feng Yuan from Washington State, USA.
Here is the largest one sent in on [ January 8, 2008 ]

This basenumber
115.254.230.534.871.709.541.072

has 24 digits
yielding the following palindromic nonagonal number
46.492.381.796.648.740.224.886.168.842.204.784.669.718.329.464
with a length of 47 digits.


bu17 A palindromic nonagonal numbers can only end with digit 1, 4, 5, 6, and 9.

bu17 There exist no palindromic nonagonals of length

2, 6, 13, 14, 15, 16, 20, 25, 27, 28, 29, 30, 31, 32, ...
(Sloane's A082722)


bu17 Sloane's A048909 gives the first numbers that are both Nonagonal and Triangular.

1, 325, 82621, 20985481, 5330229625, 1353857339341, ...
Consult also Eric Weisstein's page Nonagonal Triangular Number.

bu17 Sloane's A036411 gives the first numbers that are both Nonagonal and Square.

1, 9, 1089, 8281, 978121, 7436529...
Consult also Eric Weisstein's page Nonagonal Square Number.

bu17 Sloane's A048915 gives the first numbers that are both Nonagonal and Pentagonal.

1, 651, 180868051, 95317119801, 26472137730696901, ...
Consult also Eric Weisstein's page Nonagonal Pentagonal Number.

bu17 Sloane's A048918 gives the first numbers that are both Nonagonal and Hexagonal.

1, 325, 5330229625, 1353857339341, 22184715227362706161, ...
Consult also Eric Weisstein's page Nonagonal Hexagonal Number.

bu17 Sloane's A048921 gives the first numbers that are both Nonagonal and Heptagonal.

1, 26884, 542041975, 10928650279834, ...
Consult also Eric Weisstein's page Nonagonal Heptagonal Number.

bu17 Sloane's A048924 gives the first numbers that are both Nonagonal and Octagonal.

1, 631125, 286703855361, 130242107189808901, ...
Consult also Eric Weisstein's page Nonagonal Octagonal Number.


Sources Revealed


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.


The Table

Exhaustive search performed upto length 33



Index NrInfo BasenumberLength
Palindromic NonagonalsLength
   
Formula = n(7n–5)/2
51 Info 115.254.230.534.871.709.541.07224
46.492.381.796.648.740.224.886.168.842.204.784.669.718.329.46447
50 Info 522.755.911.437.759.066.61321
956.458.100.300.927.701.829.928.107.729.003.001.854.65942
49 Info 198.343.896.557.195.374.94921
137.691.054.555.219.967.590.095.769.912.555.450.196.73142
48 Info 21.052.483.436.370.199.81420
1.551.224.705.935.245.659.449.565.425.395.074.221.55140
47 Info 11.547.031.421.292.227.74720
466.668.771.255.085.018.151.810.580.552.177.866.66439
46 Info 10.973.370.993.981.638.98720
421.452.048.400.451.542.646.245.154.004.840.254.12439
45 Info 3.672.784.064.195.630.08719
47.212.699.737.732.795.788.759.723.773.799.621.27438
44 Info 446.339.713.063.722.37918
697.266.988.102.321.088.880.123.201.889.662.79636
43 Info 18.287.529.802.802.80617
1.170.518.112.009.402.882.049.002.118.150.71134
42 Info 16.084.074.672.143.00217
905.441.103.206.752.020.257.602.301.144.50933
41 Info 14.107.415.463.308.17917
696.567.098.690.353.494.353.096.890.765.69633
40 Info 13.543.695.809.405.31117
642.010.936.621.960.404.069.126.639.010.24633
39 Info 13.267.696.935.194.77117
616.111.236.874.618.484.816.478.632.111.61633
38 Info 4.340.322.549.81613
65.934.399.427.533.572.499.343.95626
37 Info 3.696.823.830.48713
47.832.772.517.788.771.527.723.87426
36 Info 2.053.636.735.14613
14.760.983.439.788.793.438.906.74126
35 Info 386.688.531.61012
523.348.071.674.476.170.843.32524
34 Info 172.428.811.82612
104.060.933.016.610.339.060.40124
33 Info 139.168.803.13912
67.787.845.184.648.154.878.77623
32 Info 115.589.719.27212
46.763.441.204.540.214.436.76423
31 Info 75.356.090.49411
19.874.891.310.701.319.847.89123
30 Info 21.633.254.88111
1.637.992.008.558.002.997.36122
29 Info 11.947.307.36711
499.583.536.595.635.385.99421
28 Info 1.641.773.57810
9.433.971.680.861.793.34919
27 Info 1.121.857.19210
4.404.972.454.542.794.04419
26 Info 708.609.4299
1.757.445.628.265.447.57119
25 Info 521.037.0779
950.178.723.327.871.05918
24 Info 350.096.7879
428.987.160.061.789.82418
23 Info 168.566.8539
99.451.743.334.715.49917
22 Info 446.9046
699.030.030.99612
21 Info 435.6446
664.248.842.46612
20 Info Prime!          132.6196
61.556.965.51611
19 Info 52.6425
9.698.998.96910
18 Info 18.7295
1.227.667.22110
17 Info 16.8535
994.040.4999
16 Info 16.3185
931.929.1399
15 Info 12.8705
579.696.9759
14 Info 11.4725
460.595.0649
13 Info 11.3235
448.707.8449
12 Info 4.0704
57.966.9758
11 Info 2.1014
15.444.4518
10 Info 1.4114
6.964.6967
9 Info Prime!          1.1234
4.411.1447
8 Info Prime!          1393
67.2765
7 Info 742
18.9815
6 Info 442
6.6664
5 Info Prime!          172
9693
4 Info 122
4743
3 Info 61
1113
2 Info Prime!          21
91
1 Info 11
11


Contributions

Feng Yuan (email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number 44 up to 51 [ January 8, 2008 ].

Feng Yuan (email) from Washington State, USA, discovered the palindromic nonagonals
starting from index number 1 up to 43.





[up TOP OF PAGE]


(All rights reserved) - Last modified : November 23, 2011.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com