A362464 Array of numbers read by upward antidiagonals: leading row lists sigma(i), i >= 1 (cf. A000203); the following rows give absolute values of differences of previous row.
1, 2, 3, 1, 1, 4, 1, 2, 3, 7, 1, 0, 2, 1, 6, 2, 3, 3, 5, 6, 12, 1, 3, 0, 3, 2, 4, 8, 0, 1, 2, 2, 1, 3, 7, 15, 0, 0, 1, 1, 1, 2, 5, 2, 13, 1, 1, 1, 0, 1, 0, 2, 3, 5, 18, 0, 1, 0, 1, 1, 0, 0, 2, 1, 6, 12, 4, 4, 5, 5, 6, 7, 7, 7, 9, 10, 16, 28, 0, 4, 0, 5, 0, 6, 1, 6, 1, 8, 2, 14, 14
Offset: 1
Examples
The array begins: 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, ... 2, 1, 3, 1, 6, 4, 7, 2, 5, 6, 16, 14, 10, 0, 7, ... 1, 2, 2, 5, 2, 3, 5, 3, 1, 10, 2, 4, 10, 7, ... 1, 0, 3, 3, 1, 2, 2, 2, 9, 8, 2, 6, 3, ... 1, 3, 0, 2, 1, 0, 0, 7, 1, 6, 4, 3, ... 2, 3, 2, 1, 1, 0, 7, 6, 5, 2, 1, ... 1, 1, 1, 0, 1, 7, 1, 1, 3, 1, ... ... The first few antidiagonals are: 1 2, 3 1, 1, 4 1, 2, 3, 7 1, 0, 2, 1, 6 2, 3, 3, 5, 6, 12 1, 3, 0, 3, 2, 4, 8 0, 1, 2, 2, 1, 3, 7, 15 ...
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
Programs
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Maple
See link.
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Mathematica
A362464[dmax_]:=With[{d=Reverse[NestList[Abs[Differences[#]]&,DivisorSigma[1,Range[dmax]],dmax-1]]},Array[Diagonal[d,#]&,dmax,1-dmax]];A362464[20] (* Generates 20 antidiagonals *) (* Paolo Xausa, May 10 2023 *)
Comments