A380390 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of A003988(n, k) = floor(n/k) and A380389(n - k*floor(n/k), k).

1, 2, 12, 3, 1, 13, 4, 112, 23, 14, 5, 2, 1, 12, 15, 6, 212, 113, 34, 25, 16, 7, 3, 123, 1, 35, 13, 17, 8, 312, 2, 114, 45, 12, 27, 18, 9, 4, 213, 112, 1, 23, 37, 14, 19, 10, 412, 223, 134, 115, 56, 47, 38, 29, 110, 11, 5, 3, 2, 125, 1, 57, 12, 13, 15, 111

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:
  1,  12,  13,  14,  15,  16, 17, 18, ...
  2,   1,  23,  12,  25,  13, 27, 14, ...
  3, 112,   1,  34,  35,  12, 37, 38, ...
  4,   2, 113,   1,  45,  23, 47, 12, ...
  5, 212, 123, 114,   1,  56, 57, 58, ...
  6,   3,   2, 112, 115,   1, 67, 34, ...
  7, 312, 213, 134, 125, 116,  1, 78, ...
  ...
A(3, 2) = 112 since 3/2 = 1 + 1/2.
A(4, 2) = 2 since 4/2 = 2.

Mathematica

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

Crossrefs

Cf. A003988, A372523, A380389.

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

Sequence in context: A012629 A371589 A380389 * A082827 A290100 A302389

Adjacent sequences: A380386 A380388 A380389 * A380391 A380392 A380393

Keyword

nonn,base,easy,look,tabl

Author

Stefano Spezia, Jan 23 2025

Status

approved