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

Author

Clark Kimberling, Nov 04 2007

Keywords

• nonn
• tabf

Comments

The sequence represents a para-sequence.

Examples

			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
		

References

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

Links

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

Crossrefs

Cf. A134625, A134626, A134627.

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).