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Palindromic Sums of
Cubes of Consecutive Integers
rood Sums of Squares rood Sums of Primes rood Sums of Powers rood comments


Introduction
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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 : 535, 3773, 246191642

A nice coincidence occurred with Four Consecutive Integers

59 + 60 + 61 + 62 = 242
59 3 + 60 3 + 61 3 + 62 3 = 886688

Sources Revealed
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Huen Y.K. from Singapore developed a general generating function for palindromic sums and products
of consecutive integers using concise programcode written for Macsyma 2.2.1.
Global Generating Function For Palindromic Sums and Products of Consecutive Integers.



Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :
Neil Sloane's Integer Sequences
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The regular numbers of form n3 + (n+1)3 [sums of two cubed consecutives] :
%N Centered cube numbers: n^3 + (n+1)^3. under A005898.
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The regular numbers of form n3 + (n+1)3 + (n+2)3 [sums of three cubed consecutives] :
%N n^3 + (n+1)^3 + (n+2)^3. under A027602.
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The regular numbers of form n3 + (n+1)3 + (n+2)3 + (n+3)3 [sums of four cubed consecutives] :
%N n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3. under A027603.
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The regular numbers of form n3 + (n+1)3 + (n+2)3 + (n+3)3 + (n+4)3 [sums of five cubed consecutives] :
%N n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3 + (n+4)^3. under A027604.
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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
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Index Nr Base Square Expression 
Palindromic Sums of Cubes of Consecutive Integers Length 
   
Sums of Cubes of FIVE Consecutive Integers
Searched for palindromes upto length 19.
1 ?3 + ?3 + ?3 + ?3 + ?3 
??
   
Sums of Cubes of FOUR Consecutive Integers
Searched for palindromes upto length 20.
1 593 + 603 + 613 + 623 
886.6886
   
Sums of Cubes of THREE Consecutive Integers
Searched for palindromes upto length 19.
2 163 + 173 + 183 
14.8415
1 23 + 33 + 43 
992
   
Sums of Cubes of TWO Consecutive Integers
Searched for palindromes upto length 20.
2 163 + 173 
9.0094
1 13 + 23 
91


Contributions
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(All rights reserved) - Last modified : August 2, 2004.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com