A038555 Derivative of n in base 3.

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

0,5

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A038554.

Cf. A030341.

Sequence in context: A323226 A307197 A328949 * A138108 A158777 A039970

Adjacent sequences: A038552 A038553 A038554 * A038556 A038557 A038558

Keyword

nonn,nice,easy,base

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Formula corrected by Reinhard Zumkeller, May 26 2013

Status

approved