(Palindrome)_8

Number Theory Level 3

Observe that $$9 = (9)_{10}$$ is a palindrome in base 10, and $$9 = (11)_{8}$$ is a palindrome base 8. In decimal notation, what is the next smallest integer that is a palindrome in both base 10 and base 8?

Details and assumptions

The "next smallest integer" refers to the smallest integer larger than 9 which satisfies the conditions.

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