cp's OEIS Frontend

A215879 Written in base 3, n ends in a(n) consecutive nonzero digits.

%I A215879 #39 Oct 15 2022 08:51:04
%S A215879 0,1,1,0,2,2,0,2,2,0,1,1,0,3,3,0,3,3,0,1,1,0,3,3,0,3,3,0,1,1,0,2,2,0,
%T A215879 2,2,0,1,1,0,4,4,0,4,4,0,1,1,0,4,4,0,4,4,0,1,1,0,2,2,0,2,2,0,1,1,0,4,
%U A215879 4,0,4,4,0,1,1,0,4,4,0,4,4,0,1,1,0,2,2,0,2,2,0,1,1,0,3,3,0,3,3,0,1,1,0,3,3,0,3
%N A215879 Written in base 3, n ends in a(n) consecutive nonzero digits.
%C A215879 Somehow complementary to A007949, the 3-adic valuation of n.
%C A215879 The base 2 analog of this sequence essentially coincides with the 2-adic valuation A007814 (up to a shift in the index).
%C A215879 One gets back the same sequence by concatenation of the pattern (0,1,1) successively multiplied by a(n)+1 = 1, 2, 2, 1, 3, 3, ... for n = 0, 1, 2, 3, 4, 5, .... This is equivalent to the formula (a(n)+1)*(0, 1, 1) = a(3n, 3n+1, 3n+2). - _M. F. Hasler_, Aug 26 2012, corrected Aug 23 2022
%C A215879 a(A008585(n)) = 0; a(A001651(n)) > 0. - _Reinhard Zumkeller_, Dec 28 2012
%H A215879 Reinhard Zumkeller, <a href="/A215879/b215879.txt">Table of n, a(n) for n = 0..10000</a>
%F A215879 a(3^(t+1)*k+m) = t for 3^t > m > 3^(t-1).
%F A215879 a(3n) = 0, a(3n+1) = a(3n+2) = a(n)+1. - _M. F. Hasler_, Aug 26 2012, corrected thanks to a remark from _Jianing Song_, Aug 23 2022
%e A215879 The numbers 0, 1, 2, 3, 4, 5, 6, 7 are written in base 3 as 0, 1, 2, 10, 11, 12, 20, 21 and thus end in a(0..7) = 0, 1, 1, 0, 2, 2, 0, 2 nonzero digits.
%t A215879 cnzd[n_]:=Module[{idn3=IntegerDigits[n,3],len},len=Length[idn3];Which[ idn3[[len]] == 0,0,Position[idn3,0]=={},len,True,len-Position[idn3,0] [[-1,1]]]]; Array[cnzd,110,0] (* _Harvey P. Dale_, Jun 07 2016 *)
%o A215879 (PARI) A215879(n,b=3)=n=divrem(n,b); for(c=0,oo,n[2]||return(c); n=divrem(n[1],b))
%o A215879 (PARI) a(n)=my(k);while(n%3,n\=3;k++);k \\ _Charles R Greathouse IV_, Sep 26 2013
%o A215879 (Haskell)
%o A215879 a215879 n = if t == 0 then 0 else a215879 n' + 1
%o A215879             where (n',t) = divMod n 3
%o A215879 -- _Reinhard Zumkeller_, Dec 28 2012
%o A215879 (Python)
%o A215879 def A215879(n):
%o A215879     c = 0
%o A215879     while (a:=divmod(n,3))[1]:
%o A215879         c += 1
%o A215879         n = a[0]
%o A215879     return c # _Chai Wah Wu_, Oct 15 2022
%Y A215879 The base-4, base-5 and base-10 analogs of this sequence are given in A215883, A215884 and A215887.
%Y A215879 Cf. A007089.
%K A215879 nonn,base,nice
%O A215879 0,5
%A A215879 _M. F. Hasler_, Aug 25 2012