A220465 Reverse reluctant sequence of reverse reluctant sequence A004736.

1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 4, 1, 2, 3, 1, 2, 1, 3, 4, 1, 2, 3, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 6, 1, 2, 3

Offset

1,2

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(n-k+1).

As a linear array, the sequence is a(n) = (t1*t1+3*t1+4)/2-n1, where n1=(t*t+3*t+4)/2-n, 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;
  2,1;
  1,2,1;
  3,1,2,1;
  2,3,1,2,1;
  1,2,3,1,2,1;
  ...

Prog

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

Crossrefs

Cf. A000027, A004736, A002260, A220280.

Sequence in context: A233548 A080027 A341970 * A050305 A117164 A212182

Adjacent sequences: A220462 A220463 A220464 * A220466 A220467 A220468

Keyword

easy,nonn,tabl

Author

Boris Putievskiy, Dec 15 2012

Status

approved