A123390 Triangle read by rows: n-th row starts with n and continues with half the previous value as long as that is even.

1, 2, 1, 3, 4, 2, 1, 5, 6, 3, 7, 8, 4, 2, 1, 9, 10, 5, 11, 12, 6, 3, 13, 14, 7, 15, 16, 8, 4, 2, 1, 17, 18, 9, 19, 20, 10, 5, 21, 22, 11, 23, 24, 12, 6, 3, 25, 26, 13, 27, 28, 14, 7, 29, 30, 15, 31, 32, 16, 8, 4, 2, 1, 33, 34, 17, 35, 36, 18, 9, 37, 38, 19, 39, 40, 20, 10, 5, 41, 42, 21

Offset

1,2

Comments

A fractal sequence, generated by the rule a(n) is a new maximum when a(n-1) is odd and a repetition of an earlier value when a(n-1) is even.

From Flávio V. Fernandes, Mar 13 2025: (Start)

a(n) is given by A003602(n) at A001511(n) diagram

1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9

. 1 . . . 2 . . . 3 . . . 4 . . .

. . . 1 . . . . . . . 2 . . . . .

. . . . . . . 1 . . . . . . . . .

. . . . . . . . . . . . . . . 1 .

read by backwards 2^n, which is given by A118319(n) at A001511(n) diagram

1 . 2 . 4 . 5 . 8 . 9 .11 .12 .16

. 3 . . . 6 . . .10 . . .13 . . .

. . . 7 . . . . . . .14 . . . . .

. . . . . . .15 . . . . . . . . .

. . . . . . . . . . . . . . .31 . - see formula. (End)

Links

Alois P. Heinz, Rows n = 1..10000, flattened

Formula

a(1) = 1, for n > 1, if a(n-1) is even, a(n) = a(n-1)/2, otherwise a(n) = (max_{k<n} a(k)) + 1.

Ordinal transform of A082850.

a(n) = A003602(A108918(n)). - Flávio V. Fernandes, Mar 13 2025

Example

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

Maple

T:= proc(n) local m, l; m:=n; l:= m;
      while irem(m, 2, 'm')=0 do l:=l, m od: l
    end:
seq(T(n), n=1..40);  # Alois P. Heinz, Oct 09 2015

Mathematica

Flatten[Function[n, NestWhile[Append[#, Last[#]/2] &, {n}, EvenQ[Last[#]] &]][#] & /@ Range[20]] (* Birkas Gyorgy, Apr 13 2011 *)

Crossrefs

Row lengths are A001511.

Row sums give A129527.

Cf. A120385.

Cf. A003602, A108918, A118319.

Sequence in context: A273823 A112384 A248514 * A306806 A306805 A162598

Adjacent sequences: A123387 A123388 A123389 * A123391 A123392 A123393

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Oct 13 2006

Status

approved