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A134626 Sum-fill array starting with (1,2,4,8,16,...), powers of 2.

%I A134626 #6 Feb 02 2022 10:36:43
%S A134626 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,
%T A134626 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,
%U A134626 16,10,7,14,6
%N A134626 Sum-fill array starting with (1,2,4,8,16,...), powers of 2.
%C A134626 (Row 2) is possibly A074323 except for an initial 1. The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2. Row n contains 1,2,3,...2n, but not 2n+1. Row n starts like row n of A134625; e.g., row 6 of A123625 and row of A134626 have the same first 16 terms.
%D A134626 C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
%H A134626 Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Kimberling/kimber16.html"> Self-Containing Sequences, Selection Functions, and Parasequences</a>, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.
%F A134626 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).
%e A134626 Starting with x = row 3, Step 1 gives
%e A134626 y = (1,5,4,7,3,8,5,7,2,10,8,14,6,...).
%e A134626 Delete the second 5,7,8,... leaving row 4:
%e A134626 (1,5,4,7,3,8,2,10,14,6,...).
%e A134626 Northwest corner:
%e A134626 1 2 4 8 16 32
%e A134626 1 3 2 6 4 12
%e A134626 1 4 3 5 2 8
%e A134626 1 5 4 7 3 8
%e A134626 1 6 5 9 4 11.
%Y A134626 Cf. A134625, A134627, A134628.
%K A134626 nonn,tabl
%O A134626 1,2
%A A134626 _Clark Kimberling_, Nov 04 2007