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