A077267 -id:A077267 - cp's OEIS frontend

A007089 Numbers in base 3.

0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Nonnegative integers with no decimal digit > 2. Thus nonnegative integers in base 10 whose quadrupling by normal addition or multiplication requires no carry operation. - Rick L. Shepherd, Jun 25 2009

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §2.3 Positional Notation, p. 47.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
The Unicode Consortium, Tai Xuan Jing Symbols.
Eric Weisstein's World of Mathematics, Ternary.
Wikipedia, Ternary numeral system.
Robert G. Wilson v, Letter to N. J. A. Sloane, Sep. 1992
Index entries for sequences related to Most Wanted Primes video.
Index entries for 10-automatic sequences.

Cf. A000042, A007088, A007090, A007091, A007092, A007093, A007094, A007095, A077267, A062756, A081603, A081604, A054635, A003137.

Primes when read as if in base 10: A036954.

a007089 0 = 0
a007089 n = 10 * a007089 n' + m where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 19 2012

A007089 := proc(n) option remember;
if n <= 0 then 0
else
  if (n mod 3) = 0 then 10*procname(n/3) else procname(n-1) + 1 fi
fi end:
[seq(A007089(n), n=0..729)]; # - N. J. A. Sloane, Mar 09 2019

Table[ FromDigits[ IntegerDigits[n, 3]], {n, 0, 50}]

a(n)=if(n<1,0,if(n%3,a(n-1)+1,10*a(n/3)))

a(n)=fromdigits(digits(n,3)) \\ Charles R Greathouse IV, Jan 08 2017

def A007089(n):
  n,s = divmod(n,3); t = 1
  while n: n,r = divmod(n,3); t *= 10; s += r*t
  return s # M. F. Hasler, Feb 15 2023

a(0)=0, a(n) = 10*a(n/3) if n==0 (mod 3), a(n) = a(n-1) + 1 otherwise. - Benoit Cloitre, Dec 22 2002

a(n) = 10*a(floor(n/3)) + (n mod 3) if n > 0, a(0) = 0. - M. F. Hasler, Feb 15 2023

More terms from James Sellers, May 01 2000

A062756 Number of 1's in ternary (base-3) expansion of n.

Original entry on oeis.org

0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2

Offset: 0

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001

Fixed point of the morphism: 0 ->010; 1 ->121; 2 ->232; ...; n -> n(n+1)n, starting from a(0)=0. - Philippe Deléham, Oct 25 2011

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
F. T. Adams-Watters and F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6.
Michael Gilleland, Some Self-Similar Integer Sequences
S. Northshield, An Analogue of Stern's Sequence for Z[sqrt(2)], Journal of Integer Sequences, 18 (2015), #15.11.6.
Kevin Ryde, Iterations of the Terdragon Curve, see index "dir".
Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A080846, A343785 (first differences).
Cf. A081606 (indices of !=0).
Indices of terms 0..6: A005823, A023692, A023693, A023694, A023695, A023696, A023697.
Numbers of: A077267 (0's), A081603 (2's), A160384 (1's+2's).
Other bases: A000120, A160381, A268643.

a062756 0 = 0
a062756 n = a062756 n' + m `mod` 2 where (n',m) = divMod n 3
-- Reinhard Zumkeller, Feb 21 2013

Table[Count[IntegerDigits[i, 3], 1], {i, 0, 200}]
Nest[Join[#, # + 1, #] &, {0}, 5] (* IWABUCHI Yu(u)ki, Sep 08 2012 *)

a(n)=if(n<1,0,a(n\3)+(n%3)%2) \\ Paul D. Hanna, Feb 24 2006

a(n)=hammingweight(digits(n,3)%2); \\ Ruud H.G. van Tol, Dec 10 2023

from sympy.ntheory import digits
def A062756(n): return digits(n,3)[1:].count(1) # Chai Wah Wu, Dec 23 2022

a(0) = 0, a(3n) = a(n), a(3n+1) = a(n)+1, a(3n+2) = a(n). - Vladeta Jovovic, Jul 18 2001
G.f.: (Sum_{k>=0} x^(3^k)/(1+x^(3^k)+x^(2*3^k)))/(1-x). In general, the generating function for the number of digits equal to d in the base b representation of n (0 < d < b) is (Sum_{k>=0} x^(d*b^k)/(Sum_{i=0..b-1} x^(i*b^k)))/(1-x). - Franklin T. Adams-Watters, Nov 03 2005 [For d=0, use the above formula with d=b: (Sum_{k>=0} x^(b^(k+1))/(Sum_{i=0..b-1} x^(i*b^k)))/(1-x), adding 1 if you consider the representation of 0 to have one zero digit.]
a(n) = a(floor(n/3)) + (n mod 3) mod 2. - Paul D. Hanna, Feb 24 2006

More terms from Vladeta Jovovic, Jul 18 2001

A081603 Number of 2's in ternary representation of n.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2

Offset: 0

Reinhard Zumkeller, Mar 23 2003

Fixed point of the morphism: 0 ->001; 1 ->112; 2 ->223; 3 ->334, etc., starting from a(0)=0. - Philippe Deléham, Oct 26 2011

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
F. T. Adams-Watters and F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6.
Eric Weisstein's World of Mathematics, Ternary.

Cf. A007089, A074940, A005836, A081610, A081611, A117592 (2^a(n)).

a081603 0 = 0
a081603 n = a081603 n' + m `div` 2 where (n',m) = divMod n 3
-- Reinhard Zumkeller, Feb 21 2013

A081603 := proc(n)
    local a,d ;
    a := 0 ;
    for d in convert(n,base,3) do
        if d= 2 then
            a := a+1 ;
        end if;
    end do:
    a;
end proc: # R. J. Mathar, Jul 12 2016

Table[Count[IntegerDigits[n,3],2],{n,0,6!}] (* Vladimir Joseph Stephan Orlovsky, Jul 25 2009 *)
Nest[ Flatten[# /. a_Integer -> {a, a, a + 1}] &, {0}, 5] (* Robert G. Wilson v, May 20 2014 *)
DigitCount[Range[0,120],3,2] (* Harvey P. Dale, Jul 10 2019 *)

a(n)=hammingweight(digits(n,3)\2); \\ Ruud H.G. van Tol, Dec 10 2023

from gmpy2 import digits
def A081603(n): return digits(n,3).count('2') # Chai Wah Wu, Dec 05 2024

a(n) = floor(n/2) if n < 3, otherwise a(floor(n/3)) + floor((n mod 3)/2).
A077267(n) + A062756(n) + a(n) = A081604(n);
a(n) = (A053735(n) - A062756(n))/2.

A032924 Numbers whose ternary expansion contains no 0.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 13, 14, 16, 17, 22, 23, 25, 26, 40, 41, 43, 44, 49, 50, 52, 53, 67, 68, 70, 71, 76, 77, 79, 80, 121, 122, 124, 125, 130, 131, 133, 134, 148, 149, 151, 152, 157, 158, 160, 161, 202, 203, 205, 206, 211, 212, 214, 215, 229, 230, 232, 233, 238, 239

Offset: 1

Clark Kimberling

Complement of A081605. - Reinhard Zumkeller, Mar 23 2003
Subsequence of A154314. - Reinhard Zumkeller, Jan 07 2009
The first 28 terms are the range of A059852 (Morse codes for letters, when written in base 3) union {44, 50} (which correspond to Morse codes of Ü and Ä). Subsequent terms represent the Morse code of other symbols in the same coding. - M. F. Hasler, Jun 22 2020

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, 10 (2007), Article 07.1.5., 1-13.
Clark Kimberling, Affinely recursive sets and orderings of languages, Discrete Math., 274 (2004), 147-160.
Index entries for 3-automatic sequences.

Cf. A005823, A005836, A065361, A007089, A081608, A132140, A132141.

Zeroless numbers in some other bases <= 10: A000042 (base 2), A023705 (base 4), A248910 (base 6), A255805 (base 8), A255808 (base 9), A052382 (base 10).

a032924 n = a032924_list !! (n-1)
a032924_list = iterate f 1 where
   f x = 1 + if r < 2 then x else 3 * f x'  where (x', r) = divMod x 3
-- Reinhard Zumkeller, Mar 07 2015, May 04 2012

f:= proc(n) local L,i,m;
   L:= convert(n,base,2);
   m:= nops(L);
   add((1+L[i])*3^(i-1),i=1..m-1);
end proc:
map(f, [$2..101]); # Robert Israel, Aug 04 2015

Select[Range@ 240, Last@ DigitCount[#, 3] == 0 &] (* Michael De Vlieger, Aug 05 2015 *)
Flatten[Table[FromDigits[#,3]&/@Tuples[{1,2},n],{n,5}]] (* Harvey P. Dale, May 28 2016 *)

apply( {A032924(n)=if(n<3,n,3*self()((n-1)\2)+2-n%2)}, [1..99]) \\ M. F. Hasler, Jun 22 2020

a(n) = fromdigits(apply(d->d+1,binary(n+1)[^1]), 3); \\ Kevin Ryde, Jun 23 2020

def a(n): return sum(3**i*(int(b)+1) for i, b in enumerate(bin(n+1)[:2:-1]))
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Aug 15 2022

def is_A032924(n):
    while n > 2:
       n,r = divmod(n,3)
       if r==0: return False
    return n > 0
print([n for n in range(250) if is_A032924(n)]) # M. F. Hasler, Feb 15 2023

def A032924(n): return int(bin(m:=n+1)[3:],3) + (3**(m.bit_length()-1)-1>>1) # Chai Wah Wu, Oct 13 2023

a(n) = A107680(n) + A107681(n). - Reinhard Zumkeller, May 20 2005
A081604(A107681(n)) <= A081604(A107680(n)) = A081604(a(n)) = A000523(n+1). - Reinhard Zumkeller, May 20 2005
A077267(a(n)) = 0. - Reinhard Zumkeller, Mar 02 2008
a(1)=1, a(n+1) = f(a(n)+1,a(n)+1) where f(x,y) = if x<3 and x<>0 then y, else if x mod 3 = 0 then f(y+1,y+1), else f(floor(x/3),y). - Reinhard Zumkeller, Mar 02 2008
a(2*n) = a(2*n-1)+1, n>0. - Zak Seidov, Jul 27 2009
A212193(a(n)) = 0. - Reinhard Zumkeller, May 04 2012
a(2*n+1) = 3*a(n)+1. - Robert Israel, Aug 05 2015
G.f.: x/(1-x)^2 + Sum_{m >= 1} 3^(m-1)*x^(2^(m+1)-1)/((1-x^(2^m))*(1-x)). - Robert Israel, Aug 04 2015
A065361(a(n)) = n. - Rémy Sigrist, Feb 06 2023
Sum_{n>=1} 1/a(n) = 3.4977362637842652509313189236131190039368413460747606236619907531632476445332666030262441154353753276457... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025

A081604 Number of digits in ternary representation of n.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 0

Reinhard Zumkeller, Mar 23 2003

a(n) is the length of row n in table A054635. - Reinhard Zumkeller, Sep 05 2014

			a(8) = 2 because 8 = 22_3, having 2 digits.
a(9) = 3 because 9 = 100_3, having 3 digits.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Ternary.

Cf. A003137, A007089, A030341, A049803, A054635, A062153, A070939, A080342.
Cf. A062756, A077267, A081603.
Cf. A134021, A134025, A134026, A246435.

a081604 n = if n < 3 then 1 else a081604 (div n 3) + 1
-- Reinhard Zumkeller, Sep 05 2014, Feb 21 2013

A081604 := proc(n)
    max(1,1+ilog[3](n)) ;
end proc: # R. J. Mathar, Jul 12 2016

Table[Length[IntegerDigits[n, 3]], {n, 0, 99}] (* Alonso del Arte, Dec 30 2012 *)
Join[{1},IntegerLength[Range[120],3]] (* Harvey P. Dale, Apr 07 2019 *)

a(n) = A062153(n) + 1 for n >= 1.
a(n) = A077267(n) + A062756(n) + A081603(n);
From Reinhard Zumkeller, Oct 19 2007: (Start)
0 <= A134021(n) - a(n) <= 1;
a(A134025(n)) = A134021(A134025(n));
a(A134026(n)) = A134021(A134026(n)) - 1. (End)
a(n+1) = -Sum_{k=1..n} mu(3*k)*floor(n/k). - Benoit Cloitre, Oct 21 2009
a(n) = floor(log_3(n)) + 1. - Can Atilgan and Murat Erşen Berberler, Dec 05 2012
a(n) = if n < 3 then 1 else a(floor(n/3)) + 1. - Reinhard Zumkeller, Sep 05 2014
G.f.: 1 + (1/(1 - x))*Sum_{k>=0} x^(3^k). - Ilya Gutkovskiy, Jan 08 2017

A049354 Digitally balanced numbers in base 3: equal numbers of 0's, 1's, 2's.

Original entry on oeis.org

11, 15, 19, 21, 260, 266, 268, 278, 290, 294, 302, 304, 308, 312, 316, 318, 332, 344, 348, 380, 384, 396, 410, 412, 416, 420, 424, 426, 434, 438, 450, 460, 462, 468, 500, 502, 508, 518, 520, 524, 528, 532, 534, 544, 550, 552, 572, 574, 578, 582, 586, 588, 596

Offset: 1

Harvey P. Dale

Alois P. Heinz, Table of n, a(n) for n = 1..2000

Cf. A031443, A031944.
Cf. A049354-A049360. See also A061854, A037861.
Cf. A062756, A077267, A081603.
Row n = 3 of A378000.

a049354 n = a049354_list !! (n-1)
a049354_list = filter f [1..] where
   f n = t0 == a062756 n && t0 == a081603 n where t0 = a077267 n
-- Reinhard Zumkeller, Aug 09 2014

Select[Range[600],Length[Union[DigitCount[#,3]]]== 1&]
FromDigits[#,3]&/@DeleteCases[Flatten[Permutations/@Table[PadRight[{},3n,{1,0,2}],{n,3}],1],?(#[[1]]==0&)]//Sort (* _Harvey P. Dale, May 30 2016 *)
Select[Range@5000, Differences@DigitCount[#,3]=={0,0}&] (* Hans Rudolf Widmer, Dec 11 2021 *)

from sympy.ntheory import count_digits
def ok(n): c = count_digits(n, 3); return c[0] == c[1] == c[2]
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Nov 15 2021

A062756(a(n)) = A077267(a(n)) and A081603(a(n)) = A077267(a(n)). - Reinhard Zumkeller, Aug 09 2014

A081605 Numbers having at least one 0 in their ternary representation.

Original entry on oeis.org

0, 3, 6, 9, 10, 11, 12, 15, 18, 19, 20, 21, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 45, 46, 47, 48, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 72, 73, 74, 75, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Reinhard Zumkeller, Mar 23 2003

Complement of A032924.

A212193(a(n)) <> 0. [Reinhard Zumkeller, May 04 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007089, A077267, A081607, A081606, A074940.

import Data.List (findIndices)
a081605 n = a081605_list !! (n-1)
a081605_list = findIndices (/= 0) a212193_list
-- Reinhard Zumkeller, May 04 2012

Select[Range[0,100],DigitCount[#,3,0]>0&] (* Harvey P. Dale, Aug 10 2021 *)

from itertools import count, islice
def A081605_gen(): # generator of terms
    a = -1
    for n in count(2):
        b = int(bin(n)[3:],3) + (3**(n.bit_length()-1)-1>>1)
        yield from range(a+1,b)
        a = b
A081605_list = list(islice(A081605_gen(),30)) # Chai Wah Wu, Oct 13 2023

A370853 Numbers m such that c(0) < c(1) < c(2), where c(k) = number of k's in the ternary representation of m.

Original entry on oeis.org

17, 23, 25, 53, 71, 77, 79, 134, 152, 158, 160, 161, 206, 212, 214, 215, 230, 232, 233, 238, 239, 241, 296, 314, 320, 322, 350, 386, 398, 402, 404, 422, 428, 430, 440, 452, 456, 458, 464, 466, 470, 474, 476, 478, 480, 482, 484, 485, 530, 536, 538, 554, 556

Offset: 1

Clark Kimberling, Mar 03 2024

			The ternary representation of 17 is 122, for which c(0)=0 < c(1)=1 < c(2)=2.

John Tyler Rascoe, Table of n, a(n) for n = 1..10000

Cf. A007089, A077267, A062756, A081603.

Cf. A370854, A370855, A370856, A370859, A370863, A370870.

Select[Range[1000], DigitCount[#, 3, 0] < DigitCount[#, 3, 1] < DigitCount[#, 3, 2] &]

check(m) = {my(c0=0, c1=0, c2=0, s=Vec(digits(m, 3)));
for(i=1, length(s), if(s[i]==0, c0+=1, if(s[i]==1, c1+=1, if(s[i]==2, c2+=1,))));
c0John Tyler Rascoe, Mar 11 2024

A033095 Number of 1's when n is written in base b for 2<=b<=n+1.

Original entry on oeis.org

1, 1, 3, 4, 6, 6, 9, 6, 10, 10, 12, 11, 16, 13, 15, 14, 16, 13, 18, 15, 21, 20, 21, 16, 24, 20, 23, 23, 26, 25, 32, 22, 26, 25, 25, 28, 34, 28, 32, 30, 35, 30, 37, 31, 35, 36, 35, 31, 41, 34, 37, 36, 39, 35, 43, 38, 44, 41, 42, 38, 49, 40, 43

Offset: 1

Clark Kimberling

Cf. A053735, A053737, A062756, A077267.

Cf. A033093, A033096, A033097, A033099, A033101, A033103, A033105, A033107, A033109, A033111.

f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 1]; Array[f, 63] (* Robert G. Wilson v, Nov 14 2012 *)

G.f.: x+(Sum_{b>=2} (Sum_{k>=0} x^(b^k)/(Sum_{0<=iFranklin T. Adams-Watters, Nov 03 2005

A291770 A binary encoding of the zeros in ternary representation of n.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 15, 14, 14, 13, 12, 12, 13, 12, 12, 11, 10, 10, 9, 8, 8, 9, 8, 8, 11, 10, 10, 9, 8, 8, 9, 8, 8, 7, 6, 6

Offset: 1

Antti Karttunen, Sep 11 2017

The ones in the binary representation of a(n) correspond to the nonleading zeros in the ternary representation of n. For example: ternary(33) = 1020 and binary(a(33)) = 101 (a(33) = 5).

			   n      a(n)    ternary(n)  binary(a(n))
                  A007089(n)  A007088(a(n))
  --      ----    ----------  ------------
   1        0            1           0
   2        0            2           0
   3        1           10           1
   4        0           11           0
   5        0           12           0
   6        1           20           1
   7        0           21           0
   8        0           22           0
   9        3          100          11
  10        2          101          10
  11        2          102          10
  12        1          110           1
  13        0          111           0
  14        0          112           0
  15        1          120           1
  16        0          121           0
  17        0          122           0
  18        3          200          11
  19        2          201          10
  20        2          202          10
  21        1          210           1
  22        0          211           0
  23        0          212           0
  24        1          220           1
  25        0          221           0
  26        0          222           0
  27        7         1000         111
  28        6         1001         110
  29        6         1002         110
  30        5         1010         101

Antti Karttunen, Table of n, a(n) for n = 1..59049

Cf. A007088, A007089, A077267, A289813, A289814, A291771.

Table[FromDigits[IntegerDigits[n, 3] /. k_ /; k < 3 :> If[k == 0, 1, 0], 2], {n, 110}] (* Michael De Vlieger, Sep 11 2017 *)

from sympy.ntheory.factor_ import digits
def a(n):
    k=digits(n, 3)[1:]
    return int("".join('1' if i==0 else '0' for i in k), 2)
print([a(n) for n in range(1, 111)]) # Indranil Ghosh, Sep 21 2017

(define (A291770 n) (if (zero? n) n (let loop ((n n) (b 1) (s 0)) (if (< n 3) s (let ((d (modulo n 3))) (if (zero? d) (loop (/ n 3) (+ b b) (+ s b)) (loop (/ (- n d) 3) (+ b b) s)))))))

For all n >= 0, a(A000244(n)) = A000225(n), that is, a(3^n) = (2^n) - 1. [The records in the sequence].
For all n >= 1, A000120(a(n)) = A077267(n).
For all n >= 1, A278222(a(n)) = A291771(n).

cp's OEIS Frontend

A007089 Numbers in base 3.

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A062756 Number of 1's in ternary (base-3) expansion of n.

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A081603 Number of 2's in ternary representation of n.

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A032924 Numbers whose ternary expansion contains no 0.

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A081604 Number of digits in ternary representation of n.

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A049354 Digitally balanced numbers in base 3: equal numbers of 0's, 1's, 2's.

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