A134626 Sum-fill array starting with (1,2,4,8,16,...), powers of 2.
1, 2, 1, 4, 3, 1, 8, 2, 4, 1, 16, 6, 3, 5, 1, 32, 4, 5, 4, 6, 1, 64, 12, 2, 7, 5, 7, 1, 128, 8, 8, 3, 9, 6, 8, 1, 256, 24, 6, 8, 4, 11, 7, 9, 1, 512, 16, 10, 2, 11, 5, 13, 8, 10, 1, 1024, 48, 16, 10, 7, 14, 6
Offset: 1
Examples
Starting with x = row 3, Step 1 gives y = (1,5,4,7,3,8,5,7,2,10,8,14,6,...). Delete the second 5,7,8,... leaving row 4: (1,5,4,7,3,8,2,10,14,6,...). Northwest corner: 1 2 4 8 16 32 1 3 2 6 4 12 1 4 3 5 2 8 1 5 4 7 3 8 1 6 5 9 4 11.
References
- C. 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.
Formula
Row 1 is A000079. 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).
Comments