A362913 Array of numbers read by upward antidiagonals: leading row lists phi(i), i >= 1 (cf. A000010); the following rows give absolute values of differences of previous row.
1, 0, 1, 1, 1, 2, 0, 1, 0, 2, 1, 1, 2, 2, 4, 0, 1, 2, 0, 2, 2, 1, 1, 0, 2, 2, 4, 6, 0, 1, 2, 2, 0, 2, 2, 4, 1, 1, 2, 0, 2, 2, 0, 2, 6, 0, 1, 2, 0, 0, 2, 0, 0, 2, 4, 1, 1, 0, 2, 2, 2, 4, 4, 4, 6, 10, 0, 1, 2, 2, 0, 2, 4, 0, 4, 0, 6, 4, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 8, 12, 0, 1, 2, 2
Offset: 1
Examples
The array begins: 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, ... 0, 1, 0, 2, 2, 4, 2, 2, 2, 6, 6, 8, 6, 2, 0, ... 1, 1, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 4, 2, ... 0, 1, 2, 2, 0, 2, 0, 4, 4, 2, 0, 2, 2, ... 1, 1, 0, 2, 2, 2, 4, 0, 2, 2, 2, 0, ... 0, 1, 2, 0, 0, 2, 4, 2, 0, 0, 2, ... 1, 1, 2, 0, 2, 2, 2, 2, 0, 2, ... 0, 1, 2, 2, 0, 0, 0, 2, 2, ... 1, 1, 0, 2, 0, 0, 2, 0, ... ... The first few antidiagonals are: 1 0, 1 1, 1, 2 0, 1, 0, 2 1, 1, 2, 2, 4 0, 1, 2, 0, 2, 2 1, 1, 0, 2, 2, 4, 6 0, 1, 2, 2, 0, 2, 2, 4 1, 1, 2, 0, 2, 2, 0, 2, 6 0, 1, 2, 0, 0, 2, 0, 0, 2, 4 ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened)
- N. J. A. Sloane, Maple code for Gilbreath transform and related arrays
- N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
Programs
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Mathematica
A362913[dmax_]:=With[{d=Reverse[NestList[Abs[Differences[#]]&,EulerPhi[Range[dmax]],dmax-1]]},Array[Diagonal[d,#]&,dmax,1-dmax]];A362913[20] (* Generates 20 antidiagonals *) (* Paolo Xausa, May 10 2023 *)
Comments