

A004642


Powers of 2 written in base 3.


16



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

0,2


COMMENTS

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


REFERENCES

Sloane, N. J. A. "The Persistence of a Number." J. Recr. Math. 6 (1973): 97  98


LINKS

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


MATHEMATICA

Table[FromDigits[IntegerDigits[2^n, 3]], {n, 25}] (* Alonso del Arte Dec 11 2009 *)


PROG

(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


CROSSREFS

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


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



