HOME plateWON | World!OfNumbers Palindromic Sums ofCubes of Consecutive Integers Sums of Squares Sums of Primes Sums of Powers Various Palindromic Sums

Introduction

Palindromic numbers are numbers which read the same from
left to right (forwards) as from the right to left (backwards)
Here are a few random examples : 535, 3773, 246191642

A nice coincidence occurred with Four Consecutive Integers

59 + 60 + 61 + 62 = 242
593 + 603 + 613 + 623 = 886688

Sources Revealed

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 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. 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. 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. 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. 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.

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The Table

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.
1593 + 603 + 613 + 623
886.6886

Sums of Cubes of THREE Consecutive Integers
Searched for palindromes upto length 19.
3163 + 173 + 183
14.8415
223 + 33 + 43
992
103 + 13 + 23
91

Sums of Cubes of TWO Consecutive Integers
Searched for palindromes upto length 20.
2163 + 173
9.0094
113 + 23
91

Contributions
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