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A122005 Triangle read by rows: n-th row starts with n and continues with 1/3 the previous value as long as that is an integer. 1

%I

%S 1,2,3,1,4,5,6,2,7,8,9,3,1,10,11,12,4,13,14,15,5,16,17,18,6,2,19,20,

%T 21,7,22,23,24,8,25,26,27,9,3,1,28,29,30,10,31,32,33,11,34,35,36,12,4,

%U 37,38,39,13,40,41,42,14,43,44,45,15,5,46,47,48,12,4,49,50,51,17

%N Triangle read by rows: n-th row starts with n and continues with 1/3 the previous value as long as that is an integer.

%C A fractal sequence, which is to 3 as A123390 is to 2. Row lengths are A051064 3^a(n) exactly divides 3*n. Or, 3-adic valuation of 3*n.

%F a(1) = 1, for n > 1, if 3|a(n-1) then a(n) = a(n-1)/3, otherwise a(n) = (max_{k<n} a(k)) + 1.

%e Triangle starts:

%e 1;

%e 2;

%e 3, 1;

%e 4;

%e 5;

%e 6, 2;

%e 7;

%e 8;

%e 9, 3, 1;

%e 10;

%e 11;

%e 12, 4;

%e 13;

%e 14;

%e 15, 5;

%e 16;

%t Flatten[Function[n,NestWhile[Append[#, Last[#]/3] &, {n}, Last[#]/3 == Floor[Last[#]/3] &]][#] & /@ Range[50]] (* _Birkas Gyorgy_, Apr 14 2011 *)

%Y Cf. A051064, A123390.

%K easy,nonn,tabf

%O 1,2

%A _Jonathan Vos Post_, Oct 14 2006

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)