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Search: id:A134627
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| A134627 |
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Sum-fill array starting with (1,2). |
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+0
4
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| 1, 2, 1, 3, 2, 1, 4, 3, 5, 2, 1, 5, 4, 7, 3, 8, 2, 1, 6, 5, 9, 4, 11, 7, 10, 3, 8, 2, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 18, 17, 10, 3, 8, 2, 1, 8, 7, 13, 6, 17, 11, 16, 5, 19, 14, 23, 9, 22, 4, 15, 33, 18, 35, 27, 10, 3, 2, 1, 9, 8, 15, 7, 20, 13, 19, 6, 23, 17, 28, 11, 27, 16, 21, 5, 24, 33
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2.
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REFERENCES
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C. Kimberling, Proper self-containing sequences, fractal sequences, and para-sequences, preprint, 2007.
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FORMULA
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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).
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EXAMPLE
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The initial row (1,2) begets (1,3,2) because 3 = 1+2; then
(1,3,2) begets (1,4,3,5,2) by sum-filling, etc.
First 5 rows:
1 2
1 3 2
1 4 3 5 2
1 5 4 7 3 8 2
1 6 5 9 4 1 7 10 3 8 2
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CROSSREFS
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Cf. A134625, A134626, A134628.
Adjacent sequences: A134624 A134625 A134626 this_sequence A134628 A134629 A134630
Sequence in context: A118851 A112383 A133404 this_sequence A064881 A131967 A137679
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Nov 04 2007
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