Palindromic Smith Number/Examples/123,455,554,321/Mistake

Source Work

 * The Dictionary
 * $12,345,554,321$
 * $12,345,554,321$

Mistake

 * [$12,345,554,321$ is] a palindromic Smith number.

Correction
In fact it is not.


 * $12,345,554,321 = 41 \times 239 \times 271 \times 4649$

while:
 * $1 + 2 + 3 + 4 + 5 + 5 + 5 + 4 + 3 + 2 + 1 = 35$

but:
 * $4 + 1 + 2 + 3 + 9 + 2 + 7 + 1 + 4 + 6 + 4 + 9 = 52$

The mistake can be seen in the article by, where he states:


 * There we find palindromic Smith numbers, as $12345554321$, ...

In turn, he is quoting an article in by, which states:


 * We find that $R_2^2 = 121, R_5 R_8 = 123455554321, R_4 R_{10}, R_7 R_{12}, R_4 R_{20}, R_5 R_{24}, R_5 R_{31}$, and $R_4 R_{55}$ are palindromic Smith Numbers.

Indeed, $123 \, 455 \, 554 \, 321$ is a palindromic Smith number:
 * $1 + 2 + 3 + 4 + 5 + 5 + 5 + 5 + 4 + 3 + 2 + 1 = 40 = 1 + 1 + 4 + 1 + 7 + 3 + 1 + 0 + 1 + 1 + 3 + 7 + 2 + 7 + 1$

as:
 * $123 \, 455 \, 554 \, 321 = 11 \times 41 \times 73 \times 101 \times 137 \times 271$

Hence it appears that the transcription error was indeed made by.