cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A134627 Sum-fill array starting with (1,2).

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%I A134627 #9 Feb 10 2023 10:01:35
%S A134627 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,
%T A134627 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,
%U A134627 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
%N A134627 Sum-fill array starting with (1,2).
%C A134627 The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2.
%D A134627 Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
%H A134627 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 A134627 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 A134627 The initial row (1,2) begets (1,3,2) because 3 = 1+2.
%e A134627 Then (1,3,2) begets (1,4,3,5,2) by sum-filling, etc.
%e A134627 First 5 rows:
%e A134627 1 2
%e A134627 1 3 2
%e A134627 1 4 3 5 2
%e A134627 1 5 4 7 3 8 2
%e A134627 1 6 5 9 4 1 7 10 3 8 2
%Y A134627 Cf. A134625, A134626, A134628.
%K A134627 nonn,tabf
%O A134627 1,2
%A A134627 _Clark Kimberling_, Nov 04 2007