A380389 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of the numerator and the denominator of n/k.

1, 2, 12, 3, 1, 13, 4, 32, 23, 14, 5, 2, 1, 12, 15, 6, 52, 43, 34, 25, 16, 7, 3, 53, 1, 35, 13, 17, 8, 72, 2, 54, 45, 12, 27, 18, 9, 4, 73, 32, 1, 23, 37, 14, 19, 10, 92, 83, 74, 65, 56, 47, 38, 29, 110, 11, 5, 3, 2, 75, 1, 57, 12, 13, 15, 111, 12, 112, 103, 94, 85, 76, 67, 58, 49, 310, 211, 112

Offset

1,2

Links

Stefano Spezia, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals of the array)

Example

The array begins as:
  1, 12, 13, 14, 15, 16, 17, 18, ...
  2,  1, 23, 12, 25, 13, 27, 14, ...
  3, 32,  1, 34, 35, 12, 37, 38, ...
  4,  2, 43,  1, 45, 23, 47, 12, ...
  5, 52, 53, 54,  1, 56, 57, 58, ...
  6,  3,  2, 32, 65,  1, 67, 34, ...
  7, 72, 73, 74, 75, 76,  1, 78, ...
  ...
A(6, 4) = 32 since 6/4 = 3/2.
A(6, 3) = 2 since 6/3 = 2.

Mathematica

A[n_, k_]:=If[Divisible[n, k], n/k, FromDigits[Join[IntegerDigits[Numerator[n/k]], IntegerDigits[Denominator[n/k]]]]]; Table[A[n-k+1, k], {n, 12}, {k, n}]//Flatten

Crossrefs

Cf. A003988, A372523, A380390.

Cf. A000012 (diagonal), A000027 (1st column).

Sequence in context: A012626 A012629 A371589 * A380390 A082827 A290100

Adjacent sequences: A380386 A380387 A380388 * A380390 A380391 A380392

Keyword

nonn,base,easy,look,tabl

Author

Stefano Spezia, Jan 23 2025

Status

approved