Sequence of Palindromic Lucky Numbers

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Theorem

The The sequence of lucky numbers which are also palindromic begins:

$1, 3, 7, 9, 33, 99, 111, 141, 151, 171, \ldots$

This sequence is A031161 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof

The sequence of lucky numbers begins:

$1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, \ldots$


Of these, the palindromic ones can be picked out by inspection.

$\blacksquare$


Sources