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A346497
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List of powers of 2 written in base 3 which contain no zero digits.
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3
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OFFSET
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1,2
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COMMENTS
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The listed terms are the base-3 expansions of 1, 2, 4, 8, 16, and 32768.
The program shows that there are no other terms less than 2^1000.
If it exists, a(7) > 2^(10^21). - Robert Saye, Mar 23 2022
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REFERENCES
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David Wells, "The Penguin Dictionary of Curious and Interesting Numbers" (1997), p. 123.
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LINKS
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FORMULA
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MATHEMATICA
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pwr = 1; Do[pwr = Mod[2*pwr, 3^100]; d = Union[IntegerDigits[pwr, 3]]; If[Intersection[d, {0}] == {}, Print[IntegerString[pwr, 3]]], {n, 10000000}] (* Ricardo Bittencourt, Jul 07 2021 *)
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CROSSREFS
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Cf. A102483, A004642 (all powers of 2 in base 3), A104320 (number of zeros in ternary representation of 2^n), A130693 (same problem in base 10).
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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STATUS
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approved
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