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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 07:01 EST 2018. Contains 317279 sequences. (Running on oeis4.)