A218828 Reluctant sequence of reverse reluctant sequence A004736.

1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 3, 2, 1, 4, 1, 2, 1, 3, 2, 1, 4, 3, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2

Offset

1,3

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.

Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.

Sequence A004736 is the reverse reluctant sequence of sequence 1,2,3,... (A000027).

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

T(n,k) = A004736(k) for every n.

As a linear array, the sequence is a(n) = (t1^2+3*t1+4)/2-n1, where n1=n-t(t+1)/2, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].

Example

The start of the sequence as triangle array T(n,k) is:
  1;
  1,2;
  1,2,1;
  1,2,1,3;
  1,2,1,3,2;
  1,2,1,3,2,1;
  ...

Prog

(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
n1=n-t*(t+1)/2
t1=int((math.sqrt(8*n1-7) - 1)/ 2)
m=(t1*t1+3*t1+4)/2-n1

Crossrefs

Cf. A004736, A002260, A220280.

Sequence in context: A029439 A374030 A225743 * A075117 A279387 A309852

Adjacent sequences: A218825 A218826 A218827 * A218829 A218830 A218831

Keyword

easy,nonn,tabl

Author

Boris Putievskiy, Dec 15 2012

Status

approved