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

1,2

Comments

The leading entries in the rows form A362451, the Gilbreath transform of sigma.

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

Example

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
  ...

Maple

See link.

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 *)

Crossrefs

Cf. A000203, A362451.

Sequence in context: A139343 A059247 A340940 * A244665 A194518 A023572

Adjacent sequences: A362461 A362462 A362463 * A362465 A362466 A362467

Keyword

nonn,look,tabl

Author

N. J. A. Sloane, May 09 2023

Status

approved