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A004642
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Powers of 2 written in base 3.
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16
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1, 2, 11, 22, 121, 1012, 2101, 11202, 100111, 200222, 1101221, 2210212, 12121201, 102020102, 211110211, 1122221122, 10022220021, 20122210112, 111022121001, 222122012002, 1222021101011, 10221112202022, 21220002111121, 120210012000012, 1011120101000101, 2100010202000202
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OFFSET
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0,2
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COMMENTS
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When n is odd, a(n) ends in 1, and when n is even, a(n) ends in 2, since 2^n is congruent to 1 mod 3 when n is odd and to 2 mod 3 when n is even. - Alonso del Arte Dec 11 2009
Sloane (1973) conjectured a(n) always has a 0 between the most and least significant digits if n > 15. This has been verified up to n = 10^5 (see A102483). - Alonso del Arte, Feb 20 2011
Erdos (1978) conjectured that for n > 8 a(n) has at least one 2 (see link to Terry Tao's blog). - Dmitry Kamenetsky, Jan 10 2017
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REFERENCES
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Sloane, N. J. A. "The Persistence of a Number." J. Recr. Math. 6 (1973): 97 - 98
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Jeffrey C. Lagarias, Ternary Expansions of Powers of 2, ArXiv:math/0512006v4 [math.DS], 2008.
Terry Tao, The Collatz Conjecture, 2011.
Eric Weisstein's World of Mathematics, Ternary
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MATHEMATICA
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Table[FromDigits[IntegerDigits[2^n, 3]], {n, 25}] (* Alonso del Arte Dec 11 2009 *)
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PROG
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(PARI) a(n)=fromdigits(digits(2^n, 3)) \\ M. F. Hasler, Jun 23 2018
(MAGMA) [Seqint(Intseq(2^n, 3)): n in [0..30]]; // G. C. Greubel, Sep 10 2018
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CROSSREFS
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Cf. A000079, Powers of 2 written in base 10.
Cf. A004643, ..., A004655: powers of 2 written in base 4, 5, ..., 16
Cf. A004656, A004658, A004659, ... : powers of 3 written in base 2, 4, 5, ...
Sequence in context: A263720 A235609 A018351 * A185545 A001032 A045386
Adjacent sequences: A004639 A004640 A004641 * A004643 A004644 A004645
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KEYWORD
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nonn,base,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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