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A134625 Sum-fill array starting with (1,2,3,4,...). 3
1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 3, 5, 1, 6, 7, 5, 4, 6, 1, 7, 4, 2, 7, 5, 7, 1, 8, 9, 7, 3, 9, 6, 8, 1, 9, 11, 12, 8, 4, 11, 7, 9, 1, 10, 6, 11, 2, 11, 5, 13, 8, 10, 1, 11, 13, 13, 9, 7, 14, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every row is a permutation of the positive integers. (Row 2) = A006369. The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2. In every row after row n, for each k<=n, k+1 precedes k and all the numbers between k+1 and k exceed k+1.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..62.

Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, unpublished manuscript, 2007, cached copy, with permission.

FORMULA

Row 1 is the sequence of positive integers. 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

Starting with x = row 1, Step 1 gives

y = (1,3,2,5,3,7,4,9,5,11,6,13,...).

Delete the second 3,5,7,... leaving row 2:

(1,3,2,5,7,4,9,11,6,13,...).

Northwest corner:

1 2 3 4 5 6 7 8

1 3 2 5 7 4 9 11

1 4 3 5 2 7 12 11

1 5 4 7 3 8 2 9

1 6 5 9 4 11 7 10.

CROSSREFS

Cf. A134626, A134627, A134628.

Sequence in context: A195915 A219158 A049834 * A325477 A277227 A054531

Adjacent sequences:  A134622 A134623 A134624 * A134626 A134627 A134628

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Nov 04 2007

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)