

A122005


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


1



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

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..75.


FORMULA

a(1) = 1, for n > 1, if 3a(n1) then a(n) = a(n1)/3, otherwise a(n) = (max_{k<n} a(k)) + 1.


EXAMPLE

Triangle starts:
1;
2;
3, 1;
4;
5;
6, 2;
7;
8;
9, 3, 1;
10;
11;
12, 4;
13;
14;
15, 5;
16;


MATHEMATICA

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


CROSSREFS

Cf. A051064, A123390.
Sequence in context: A055442 A055439 A329849 * A306353 A117385 A071517
Adjacent sequences: A122002 A122003 A122004 * A122006 A122007 A122008


KEYWORD

easy,nonn,tabf


AUTHOR

Jonathan Vos Post, Oct 14 2006


STATUS

approved



