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, 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, 16, 49, 50, 51, 17, 52, 53, 54, 18, 6, 2, 55, 56, 57, 19, 58, 59, 60, 20

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, 3-adic valuation of 3*n.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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.

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 *)
Table[Select[NestWhileList[#/3&, n, IntegerQ[#]&], IntegerQ], {n, 60}]//Flatten (* Harvey P. Dale, May 17 2026 *)

Crossrefs

Cf. A051064, A123390.

Sequence in context: A055439 A389898 A329849 * A362506 A306353 A117385

Adjacent sequences: A122002 A122003 A122004 * A122006 A122007 A122008

Keyword

easy,nonn,tabf

Author

Jonathan Vos Post, Oct 14 2006

Extensions

Corrected and extended by Harvey P. Dale, May 17 2026

Status

approved