3-digit palindromes that are palindromic in smaller bases

 
 
Here are 32   3-digit palindromes in base 10 whose equivalents in smaller bases b,
2 \leq b \leq 9   are also palindromic:

111 base-10 = 303 base-6

121 base-10 = 11111 base-3 = 232 base-7 = 171 base-8

141 base-10 = 353 base-6

151 base-10 = 12121 base-3

171 base-10 = 333 base-7

191 base-10 = 515 base-6 = 232 base-9

212 base-10 = 21212 base-3

242 base-10 = 22222 base-3 = 464 base-7

252 base-10 = 2002 base-5

282 base-10 = 2112 base-5 = 343 base-9

292 base-10 = 565 base-7 = 444 base-8

313 base-10 = 100111001 base-2

333 base-10 = 515 base-8

343 base-10 = 1331 base-6

373 base-10 = 11311 base-4 = 565 base-8 = 454 base-9

393 base-10 = 12021 base-4

414 base-10 = 636 base-8

434 base-10 = 2002 base-6

464 base-10 = 565 base-9

484 base-10 = 122221 base-3

555 base-10 = 676 base-9

585 base-10 = 1001001001 base-2 = 1111 base-8

626 base-10 = 10001 base-5

646 base-10 = 787 base-9

656 base-10 = 220022 base-3 = 808 base-9

666 base-10 = 22122 base-4

676 base-10 = 10201 base-5

717 base-10 = 1011001101 base-2

757 base-10 = 1001001 base-3

777 base-10 = 3333 base-6

868 base-10 = 4004 base-6

939 base-10 = 32223 base-4

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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