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A038555 Derivative of n in base 3.

%I A038555 #23 Nov 01 2024 15:07:51
%S A038555 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,
%T A038555 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,
%U A038555 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
%N A038555 Derivative of n in base 3.
%H A038555 Reinhard Zumkeller, <a href="/A038555/b038555.txt">Table of n, a(n) for n = 0..10000</a>
%F A038555 Write n in ternary, replace each pair of adjacent digits by their modulo 3 sum.
%e A038555 15 = 120 in ternary, derivative is 02 = 2, so a(15)=2.
%t A038555 Table[FromDigits[Mod[Total[#],3]&/@Partition[IntegerDigits[n,3],2,1],3],{n,0,100}] (* _Harvey P. Dale_, Nov 01 2024 *)
%o A038555 (Haskell)
%o A038555 a038555 n = foldr (\d v -> v * 3 + d) 0 $
%o A038555    zipWith (\x y -> (x + y) `mod` 3) ts $ tail ts
%o A038555    where ts = a030341_row n
%o A038555 -- _Reinhard Zumkeller_, May 26 2013
%o A038555 (J) ab3 =: 3&#.^:_1
%o A038555 sp =: 2&(+/\)"1
%o A038555 > (3 | sp)&.ab3&.> ;/ i. 100 NB. _Stephen Makdisi_, May 26 2018
%Y A038555 Cf. A038554.
%Y A038555 Cf. A030341.
%K A038555 nonn,nice,easy,base
%O A038555 0,5
%A A038555 _N. J. A. Sloane_
%E A038555 More terms from _Erich Friedman_
%E A038555 Formula corrected by _Reinhard Zumkeller_, May 26 2013