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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $111$