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Palindromic Tetrahedrals | |||

Factorization Palindromic Cubes |

So, this line is for experts only

The best way to get a 'structural' insight as how to imagine tetrahedrals is to visit these sites :

base x ( base + 1 ) x ( base + 2 )------------------------------------------ 6

- From Eric Weisstein's Math Encyclopedia : Tetrahedral Number
- A real life application explained in this kite-site.

On sci.math there was a discussion a while ago about a nonpalindromic relationship :

Question: What numbers are both Triangular and Tetrahedral ?

Answer: The only possible ones are 0, 1, 10, 120, 1540 and 7140 (Sloane's A027568).Triangular basenumbers are 0, 1, 4, 15, 55 and 119 Tetrahedral basenumbers are 0, 1, 3, 8, 20 and 34 Proof: E.T. Avanesov (Rumanian?) proved in 1966 that the above numbers constitute the complete set of solutions.

Acta Arithmetica, vol. 12, 409-420. The proof is particularly abstruse.

All tetrahedral numbers can only end with **1**, **4**, **5**, **6** or **9**. Confert the square numbers !

The product of three consecutive integers is always divisible by 6.

A good source for such statements is *"The Book of Numbers"*

by John H. Conway and Richard K. Guy.

Click on the image on the left for more background about the book.

The book can be ordered at 'www.amazon.com'.

but also to primes in one of the following manners :

Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :P. De Geest] entries to the table.Click here to view some entries to the table about palindromes. |

[ *June 10, 2021* ].

Patrick De Geest's search program exhaustively scanned all possible palindromic candidates up to length 41.

[ *June 1, 2002* ]

Walter Schneider (email) made a quick search up to basenumber 10^10.

No new palindromic solution was found.

Index Nr | Info |
Basenumber | Length |
---|---|---|---|

Palindromic Tetrahedrals | Length | ||

Formula (n)(n+1)(n+2)/6 | |||

6 | Info | 336 | 3 |

6.378.736 | 7 | ||

5 | Info | 21 | 2 |

1.771 | 4 | ||

4 | Info | Prime! 17 | 2 |

969 | 3 | ||

3 | Info | Prime! 2 | 1 |

4 | 1 | ||

2 | Info | 1 | 1 |

1 | 1 | ||

1 | Info | 0 | 1 |

0 | 1 |

Kevin Brown informs me that he has more info about tetrahedral palindromes in other base representations.

Read his article :

On General Palindromic Numbers

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Patrick De Geest - Belgium - Short Bio - Some Pictures

E-mail address : pdg@worldofnumbers.com