

A004642


Powers of 2 written in base 3.


22



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 (see A102483 and A346497).
Erdős (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

N. J. A. Sloane, The Persistence of a Number, J. Recr. Math. 6 (1973), 9798.


LINKS

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.


KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



