The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (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 (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), 97-98. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Yagub N. Aliyev, Digits of powers of 2 in ternary numeral system, Notes on Number Theory and Discrete Mathematics, Vol. 29, No. 3 (2023), 474-485. Paul Erdős, Some unconventional problems in number theory, Mathematics Magazine, Vol. 52, No. 2 (1979), pp. 67-70. Jeffrey C. Lagarias, Ternary Expansions of Powers of 2, Journal of the London Mathematical Society, Vol. 79, No. 3 (2009), pp. 562-588; arXiv preprint, arXiv:math/0512006 [math.DS], 2005-2008. Terry Tao, The Collatz Conjecture, Littlewood-Offord theory, and powers of 2 and 3, 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, ..., A004663: powers of 3 written in base 2, 4, 5, ..., 9. Sequence in context: A263720 A235609 A018351 * A346497 A185545 A001032 Adjacent sequences: A004639 A004640 A004641 * A004643 A004644 A004645 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 08:12 EST 2023. Contains 367515 sequences. (Running on oeis4.)