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Vepir

I study Mathematics and Computer Science.

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Contact: vesm@tuta.io

P.S. Can you find a palindrome in four consecutive number bases?

$$3 = 11_2$$ $$10 = 101_3=22_4$$ $$178 = 454_6 =343_7 = 262_8$$ $$? = {x}_{b+1} = {y}_{b+2} = {z}_{b+3} = {w}_{b+4}$$

If it has an equal number of digits $l$ in all four consecutive number bases, then $l\ge 15$ (see A323742 for this bound). Otherwise, it has a non-constant number of digits and is larger than $10^{12}$, if it exists (see A327810 for this bound).

P.S.P.S. Can you find a palindrome in three consecutive number bases but with a non-constant number of digits?

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