A007089 -id:A007089 - cp's OEIS frontend

A190128 Numbers 1 through 10000 sorted lexicographically in ternary representation.

1, 3, 9, 27, 81, 243, 729, 2187, 6561, 6562, 6563, 2188, 6564, 6565, 6566, 2189, 6567, 6568, 6569, 730, 2190, 6570, 6571, 6572, 2191, 6573, 6574, 6575, 2192, 6576, 6577, 6578, 731, 2193, 6579, 6580, 6581, 2194, 6582, 6583, 6584, 2195, 6585, 6586, 6587, 244

Offset: 1

Reinhard Zumkeller, May 06 2011

A190129 = inverse permutation: a(A190129(n)) = A190129(a(n)) = n;

a(n) <> n for n > 1.

			a(12) = 2188 -> 10000001  [tern];
a(13) = 6564 -> 100000010 [tern];
a(14) = 6565 -> 100000011 [tern];
a(15) = 6566 -> 100000012 [tern];
a(16) = 2189 -> 10000002  [tern];
a(17) = 6567 -> 100000020 [tern];
a(18) = 6568 -> 100000021 [tern];
a(19) = 6569 -> 100000022 [tern];
a(20) =  730 -> 1000001   [tern];
a(21) = 2190 -> 10000010  [tern];
largest term a(5164) = 10000 -> 111201101 [tern];
last term a(10000) = 6560 -> 22222222 [tern], largest term lexicographically.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (full sequence)
Eric Weisstein's World of Mathematics, Lexicographic Order
Eric Weisstein's World of Mathematics, Ternary
Wikipedia, Lexicographical order
Wikipedia, Ternary numeral system

Cf. A007089; A190126 (base 2), A190130 (base 8), A190016 (base 10), A190132 (base 12), A190134 (base 16).

import Data.Ord (comparing)
import Data.List (sortBy)
a190128 n = a190128_list !! (n-1)
a190128_list = sortBy (comparing (show . a007089)) [1..10000]

A242399 Write n and 3n in ternary representation and add all trits modulo 3.

Original entry on oeis.org

0, 4, 8, 12, 16, 11, 24, 19, 23, 36, 40, 44, 48, 52, 47, 33, 28, 32, 72, 76, 80, 57, 61, 56, 69, 64, 68, 108, 112, 116, 120, 124, 119, 132, 127, 131, 144, 148, 152, 156, 160, 155, 141, 136, 140, 99, 103, 107, 84, 88, 83, 96, 91, 95, 216, 220, 224, 228, 232

Offset: 0

Reinhard Zumkeller, May 13 2014

			n = 25, 3*n = 75:
.  A007089(25) =  221
.  A007089(75) = 2210
.   add trits    ----
.    modulo 3    2101 = A007089(64), hence a(25) = 64.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
P. Mathonet, M. Rigo, M. Stipulanti and N. Zénaïdi, On digital sequences associated with Pascal's triangle, arXiv:2201.06636 [math.NT], 2022.
Eric Weisstein's World of Mathematics, Ternary.
Wikipedia, Ternary numeral system
Index entries for sequences related to carryless arithmetic

Cf. A004488, A007089, A008586, A030341, A048724, A242400, A242407.

Row / column 4 of A325820.

a242399 n = foldr (\t v -> 3 * v + t) 0 $
                  map (flip mod 3) $ zipWith (+) ([0] ++ ts) (ts ++ [0])
            where ts = a030341_row n

a(n) <= 4*n; a(m) = 4*m iff m is a term of A242407.

a(n) = A008586(n) - A242400(n).

A031948 Numbers with exactly two distinct base-3 digits.

Original entry on oeis.org

3, 5, 6, 7, 9, 10, 12, 14, 16, 17, 18, 20, 22, 23, 24, 25, 27, 28, 30, 31, 36, 37, 39, 41, 43, 44, 49, 50, 52, 53, 54, 56, 60, 62, 67, 68, 70, 71, 72, 74, 76, 77, 78, 79, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 122

Offset: 1

Clark Kimberling

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007089.

filter:= n -> nops(convert(convert(n,base,3),set))=2:
select(filter, [$1..200]); # Robert Israel, Nov 29 2017

Select[Range[150],Length[Union[IntegerDigits[#,3]]]==2&] (* Harvey P. Dale, Nov 25 2023 *)

A037381 Numbers k such that every base-3 digit of k is a base-5 digit of k.

Original entry on oeis.org

1, 2, 7, 27, 28, 30, 35, 40, 51, 54, 55, 60, 71, 121, 127, 132, 135, 136, 137, 138, 139, 142, 147, 152, 157, 160, 161, 175, 176, 177, 178, 179, 180, 185, 190, 195, 202, 210, 211, 212, 214, 227, 232, 235, 238, 239, 242, 251, 255

Offset: 1

Clark Kimberling

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

Cf. A007089, A007091.

Cf. A037380, A037382, A037383, A037384, A037385, A037386.

import Data.List ((\\), nub)
a037381 n = a037381_list !! (n-1)
a037381_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 5 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Select[Range[300],SubsetQ[IntegerDigits[#,5],IntegerDigits[#,3]]&] (* Harvey P. Dale, Dec 31 2017 *)

A037382 Numbers k such that every base-3 digit of k is a base-6 digit of k.

Original entry on oeis.org

1, 2, 8, 13, 26, 36, 37, 38, 39, 40, 44, 48, 49, 50, 52, 53, 68, 72, 73, 74, 78, 79, 80, 109, 121, 152, 157, 182, 218, 224, 228, 229, 230, 231, 232, 233, 236, 242, 243, 244, 246, 247, 248, 252, 253, 254, 255, 256, 264, 270, 282, 288

Offset: 1

Clark Kimberling

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

Cf. A007089, A007092.

Cf. A037380, A037381, A037383, A037384, A037385, A037386.

import Data.List ((\\), nub)
a037382 n = a037382_list !! (n-1)
a037382_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 6 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Select[Range[300],SubsetQ[IntegerDigits[#,6],IntegerDigits[#,3]]&] (* Harvey P. Dale, Jun 05 2015 *)

A037383 Numbers k such that every base-3 digit of k is a base-7 digit of k.

Original entry on oeis.org

1, 2, 13, 51, 63, 67, 68, 79, 84, 91, 99, 105, 134, 205, 211, 246, 252, 345, 351, 352, 354, 355, 357, 358, 359, 360, 361, 362, 363, 364, 366, 373, 380, 387, 394, 401, 406, 441, 442, 443, 444, 445, 446, 447, 448, 449, 454, 455, 457

Offset: 1

Clark Kimberling

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

Cf. A007089, A007093.

Cf. A037380, A037381, A037382, A037384, A037385, A037386.

import Data.List ((\\), nub)
a037383 n = a037383_list !! (n-1)
a037383_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 7 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Select[Range[500],Complement[Union[IntegerDigits[#,3]],Union[IntegerDigits[#,7]]]=={}&] (* Harvey P. Dale, Jan 28 2024 *)

upto(N) = my(s7); [n|n<-[1..N], setunion(Set(digits(n, 3)), s7=Set(digits(n, 7)))==s7]; \\ Ruud H.G. van Tol, May 09 2024

A037384 Numbers k such that every base-3 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 13, 17, 26, 66, 80, 112, 120, 121, 122, 129, 136, 161, 168, 202, 242, 328, 394, 401, 458, 514, 522, 528, 529, 530, 531, 532, 533, 534, 535, 538, 546, 554, 562, 570, 578, 592, 610, 634, 640, 641, 642, 643, 644, 645, 646, 647

Offset: 1

Clark Kimberling

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A007089, A007094.

Cf. A037380, A037381, A037382, A037383, A037385, A037386.

import Data.List ((\\), nub)
a037384 n = a037384_list !! (n-1)
a037384_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

b3b8Q[n_]:=Module[{b3=Union[IntegerDigits[n,3]],b8=Union[ IntegerDigits[n,8]]}, And@@Table[ MemberQ[b8,b3[[i]]],{i,Length[b3]}]]; Select[Range[700],b3b8Q] (* Harvey P. Dale, Apr 17 2013 *)

is(n)=#setminus(Set(digits(n,3)), Set(digits(n,8)))==0 \\ Charles R Greathouse IV, Feb 11 2017

A037385 Numbers k such that every base-3 digit of k is a base-9 digit of k.

Original entry on oeis.org

1, 2, 9, 13, 18, 26, 81, 82, 83, 84, 85, 90, 99, 108, 117, 121, 162, 163, 164, 168, 170, 171, 180, 216, 234, 242, 244, 252, 325, 333, 488, 504, 650, 666, 729, 730, 731, 732, 733, 738, 739, 740, 741, 742, 747, 748, 749, 750, 751

Offset: 1

Clark Kimberling

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

Cf. A007089, A007095.

Cf. A037380, A037381, A037382, A037383, A037384, A037386.

import Data.List ((\\), nub)
a037385 n = a037385_list !! (n-1)
a037385_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 9 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Select[Range[1000],SubsetQ[IntegerDigits[#,9],IntegerDigits[#,3]]&] (* Harvey P. Dale, Dec 19 2015 *)

A088151 Value of n-th digit in ternary representation of n^n.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 0, 1, 1

Offset: 0

Reinhard Zumkeller, Sep 20 2003

a(n)=d(n) with n^n = Sum(d(k)*3^k: 0<=d(k)<3, k>=0).

			n=7, 7^7=3110367 -> '1112211200121', '111221-------': a(7)=1.

Eric Weisstein's World of Mathematics, Ternary

Cf. A007089, A000312, A088150, A088152, A088153, A088154, A088155, A088156, A088157.

a(n) = floor(n^n / 3^n) mod 3.

A125291 Number of partitions of n into positive digit values of its ternary representation.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 6, 1, 1, 8, 8, 9, 9, 1, 10, 1, 11, 12, 12, 1, 13, 1, 1, 1, 15, 1, 1, 17, 17, 18, 18, 1, 1, 20, 1, 1, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 1, 28, 1, 29, 30, 30, 1, 31, 1, 32, 33, 33, 34, 34, 35, 35, 36, 36, 1, 37, 1, 38, 39, 39, 1, 40, 1, 1, 1, 42

Offset: 1

Reinhard Zumkeller, Nov 26 2006

a(A125292(n))=1; a(A125293(n))=floor((n+2)/2)=A008619(n).

R. Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Ternary

Cf. A007089, A061827.

a(n) = 1 + floor(n/2) * (1 - 0^(A062756(n)*A081603(n))).

cp's OEIS Frontend

A190128 Numbers 1 through 10000 sorted lexicographically in ternary representation.

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A242399 Write n and 3n in ternary representation and add all trits modulo 3.

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Formula

A031948 Numbers with exactly two distinct base-3 digits.

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A037381 Numbers k such that every base-3 digit of k is a base-5 digit of k.

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Mathematica

A037382 Numbers k such that every base-3 digit of k is a base-6 digit of k.

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Mathematica

A037383 Numbers k such that every base-3 digit of k is a base-7 digit of k.

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PARI

A037384 Numbers k such that every base-3 digit of k is a base-8 digit of k.

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Mathematica

PARI

A037385 Numbers k such that every base-3 digit of k is a base-9 digit of k.

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Haskell

Mathematica

A088151 Value of n-th digit in ternary representation of n^n.

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