A030341 -id:A030341 - cp's OEIS frontend

A047469 Numbers that are congruent to {0, 1, 2} mod 8.

0, 1, 2, 8, 9, 10, 16, 17, 18, 24, 25, 26, 32, 33, 34, 40, 41, 42, 48, 49, 50, 56, 57, 58, 64, 65, 66, 72, 73, 74, 80, 81, 82, 88, 89, 90, 96, 97, 98, 104, 105, 106, 112, 113, 114, 120, 121, 122, 128, 129, 130, 136, 137, 138, 144, 145, 146, 152, 153, 154

Offset: 1

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A030341.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

[n : n in [0..150] | n mod 8 in [0..2]]; // Wesley Ivan Hurt, Jun 09 2016

A047469:=n->(24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047469(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Select[Range[0, 150], MemberQ[{0, 1, 2}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

PARI
```
a(n)=n+(n-1)\3*5-1
```

G.f.: x*(1 + x + 6*x^2)/((1 - x)*(1 - x^3)).
a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k) = 8*3^(k-1) for k>0. - Philippe Deléham, Oct 24 2011
From Wesley Ivan Hurt, Jun 09 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-6, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)
a(n) = n + 5*floor((n-1)/3) - 1. - Bruno Berselli, Feb 06 2017

A262412 A262411 in ternary representation.

Original entry on oeis.org

1, 10, 11, 12, 2, 20, 22, 21, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 202, 201, 212, 210, 221, 211, 222, 220, 1002, 1001, 1000, 1010, 1011, 1012, 1021, 1020, 1101, 1022, 1102, 1110, 1100, 1111, 1112, 1120, 1121, 1122, 1201, 1200, 1211, 1202, 1212

Offset: 1

Reinhard Zumkeller, Sep 22 2015

a(n) = A007089(A262411(n)).

			See A262411.

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

Cf. A030341, A007089, A262411.

import Data.List (inits, tails, intersect, delete)
a262412 n = a262412_list !! (n - 1)
a262412_list = 1 : f [1] (drop 2 a030341_tabf) where
   f xs tss = g tss where
     g (ys:yss) | null (intersect its $ tail $ inits ys) &&
                  null (intersect tis $ init $ tails ys) = g yss
                | otherwise = (foldr (\t v -> 10 * v + t) 0 ys) :
                              f ys (delete ys tss)
     its = init $ tails xs; tis = tail $ inits xs
-- Reinhard Zumkeller, Sep 22 2015

A038555 Derivative of n in base 3.

Original entry on oeis.org

0, 0, 0, 1, 2, 0, 2, 0, 1, 3, 4, 5, 7, 8, 6, 2, 0, 1, 6, 7, 8, 1, 2, 0, 5, 3, 4, 9, 10, 11, 13, 14, 12, 17, 15, 16, 21, 22, 23, 25, 26, 24, 20, 18, 19, 6, 7, 8, 1, 2, 0, 5, 3, 4, 18, 19, 20, 22, 23, 21, 26, 24, 25, 3, 4, 5, 7, 8, 6, 2, 0, 1, 15, 16, 17, 10, 11, 9, 14, 12, 13, 27, 28, 29

Offset: 0

N. J. A. Sloane

			15 = 120 in ternary, derivative is 02 = 2, so a(15)=2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A038554.

Cf. A030341.

a038555 n = foldr (\d v -> v * 3 + d) 0 $
   zipWith (\x y -> (x + y) `mod` 3) ts $ tail ts
   where ts = a030341_row n
-- Reinhard Zumkeller, May 26 2013

ab3 =: 3&#.^:_1
sp =: 2&(+/\)"1
> (3 | sp)&.ab3&.> ;/ i. 100 NB. Stephen Makdisi, May 26 2018

Table[FromDigits[Mod[Total[#],3]&/@Partition[IntegerDigits[n,3],2,1],3],{n,0,100}] (* Harvey P. Dale, Nov 01 2024 *)

Write n in ternary, replace each pair of adjacent digits by their modulo 3 sum.

More terms from Erich Friedman

Formula corrected by Reinhard Zumkeller, May 26 2013

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A047469 Numbers that are congruent to {0, 1, 2} mod 8.

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A262412 A262411 in ternary representation.

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A038555 Derivative of n in base 3.

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