A134628 Sum-fill array starting with (2,1).

2, 1, 2, 3, 1, 2, 5, 3, 4, 1, 2, 7, 5, 8, 3, 4, 1, 2, 9, 7, 12, 5, 13, 8, 11, 3, 4, 1, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 14, 3, 4, 1, 2, 13, 11, 20, 9, 25, 16, 23, 7, 26, 19, 31, 12, 29, 17, 22, 5, 18, 34, 21, 8, 14, 3, 4, 1, 2, 15, 13, 24, 11, 31, 20, 29, 9, 34, 25, 41, 16, 39, 23

Offset

1,1

Comments

The sequence represents a para-sequence.

References

Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.

Links

Table of n, a(n) for n=1..85.

Clark Kimberling, Self-Containing Sequences, Selection Functions, and Parasequences, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.

Formula

Row n>=2 is produced from row n by the sum-fill operation, defined on an arbitrary infinite or finite sequence x = (x(1), x(2), x(3), ...) by the following two steps: Step 1. Form the sequence x(1), x(1)+x(2), x(2), x(2)+x(3), x(3), x(3)+x(4), ...; i.e., fill the space between x(n) and x(n+1) by their sum. Step 2. Delete duplicates; i.e., letting y be the sequence resulting from Step 1, if y(n+h)=y(n) for some h>=1, then delete y(n+h).

Example

The initial row (2,1) begets (2,3,1) because 3 = 2+1.
Then (2,3,1) begets (2,5,3,4,1) by sum-filling, etc.
First 5 rows:
2 1
2 3 1
2 5 3 4 1
2 7 5 8 3 4 1
1 6 5 9 4 1 7 10 3 8 2

Crossrefs

Cf. A134625, A134626, A134627.

Sequence in context: A178030 A131879 A172288 * A064882 A065158 A364842

Adjacent sequences: A134625 A134626 A134627 * A134629 A134630 A134631

Keyword

nonn,tabf

Author

Clark Kimberling, Nov 04 2007

Status

approved