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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy
• base

Examples

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

Links

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

Crossrefs

Cf. A038554.

Cf. A030341.

Programs

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

Mathematica

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

Formula

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

Extensions

More terms from Erich Friedman

Formula corrected by Reinhard Zumkeller, May 26 2013