Question

is the sequence of powers of 3 is an arithmetic sequence. why?​

Answer 1

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The sums of distinct powers of three form a Stanley sequence, the lexicographically smallest sequence that does not contain an arithmetic progression of three elements. A conjecture of Paul Erdős states that this sequence contains no powers of two other than 1, 4, and 256.

Answer 2

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$\mapsto$ The sums of distinct powers of three form a Stanley sequence, the lexicographically smallest sequence that does not contain an arithmetic progression of three elements. A conjecture of Paul Erdős states that this sequence contains no powers of two other than 1, 4, and 256.

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