Numbers whose Digits are Unchanged when Subtracting Reversal

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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Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1980$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1980$