What is the smallest palindrome that is the cube of a non-palindromic number?

Not seeing a solution in a spreadsheet, and several ill-constructed programs, one program seemed to work but the ‘non-palindromic’ count had reached a 9- or 10-digit number.  With a D3 rating something was wrong.

The problem is asking for “a palindrome that is the cube of something not palindromic”.   That was telling me that I was working with integers, but was I?

Taking that wording at face value I supposed, since a single digit is considered to be a palindrome 1 cannot be considered as both it and its root are palindromes.  2 however is the cube of 2^(1/3).

While searching for palindromic scripts I happened upon something stating that a certain value was the only known one to generate a palindromic cube, and emphasis on the word cube.

 

Editing my listing I the program stopped at the said result: 2201^3

 ‘ QB64 listing

CLS

DIM SHARED a AS DOUBLE
DIM SHARED k AS DOUBLE
DIM SHARED p$
DIM SHARED p
a = 1

done = 0
DO
  k = a
  PalTest
  IF p = 0 THEN
    k = a ^ 3
    PalTest

    IF p = 1 THEN
      done = 1
      PRINT a, a ^ 3
      PRINT "done"
    END IF

  END IF
  a = a + 1
LOOP WHILE (done <> 1)

SUB PalTest
p = 0
p$ = LTRIM$(STR$(k))
ln = LEN(p$)
b = 1
DO
  IF MID$(p$, b, 1) = MID$(p$, ln - b + 1, 1) THEN
    p = 1
  ELSE
    p = 0
  END IF
  b = b + 1
LOOP WHILE (b < ln AND p <> 0)
END SUB

Posted by brianjn on 2012-06-16 21:19:13