Numbers whose Digits are Unchanged when Subtracting Reversal

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Theorem

The following sequence consists of the integers which have the property that subtraction of their reversals results in anagrams of them:

$954, 1980, 2961, 3870, 5823, 7641, 9108, 19980, 29880, 29961, 32760, \ldots$

This sequence is A121969 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof

\(\ds 954 - 459\) \(=\) \(\ds 495\)
\(\ds 1980 - 0891\) \(=\) \(\ds 1089\)
\(\ds 2961 - 1692\) \(=\) \(\ds 1269\)
\(\ds 3870 - 0783\) \(=\) \(\ds 3087\)
\(\ds 5823 - 3285\) \(=\) \(\ds 2538\)
\(\ds 7641 - 1467\) \(=\) \(\ds 6174\)
\(\ds 9108 - 8019\) \(=\) \(\ds 1089\)
\(\ds 19 \, 980 - 08 \, 991\) \(=\) \(\ds 10 \, 989\)
\(\ds 29 \, 880 - 08 \, 892\) \(=\) \(\ds 20 \, 988\)
\(\ds 29 \, 961 - 16 \, 992\) \(=\) \(\ds 12 \, 969\)
\(\ds 32 \, 760 - 06 \, 732\) \(=\) \(\ds 26 \, 037\)


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In particular: that there are no more in between these
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Sources

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