A367825 Array read by ascending antidiagonals: A(n, k) is the denominator of (R(n) - k)/(n + k), where R(n) is the digit reversal of n, with A(0, 0) = 1.
1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 1, 2, 1, 1, 5, 5, 5, 5, 1, 1, 3, 3, 1, 3, 3, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 4, 2, 4, 1, 4, 2, 4, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 10, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 4, 6, 12, 2, 3, 6, 1, 6, 3, 2, 3, 6, 1
Offset: 0
Examples
The array of the fractions begins: 1, -1, -1, -1, -1, -1, -1, -1, ... 1, 0, -1/3, -1/2, -3/5, -2/3, -5/7, -3/4, ... 1, 1/3, 0, -1/5, -1/3, -3/7, -1/2, -5/9, ... 1, 1/2, 1/5, 0, -1/7, -1/4, -1/3, -2/5, ... 1, 3/5, 1/3, 1/7, 0, -1/9, -1/5, -3/11, ... 1, 2/3, 3/7, 1/4, 1/9, 0, -1/11, -1/6, ... 1, 5/7, 1/2, 1/3, 1/5, 1/11, 0, -1/13, ... 1, 3/4, 5/9, 2/5, 3/11, 1/6, 1/13, 0, ... ... The array of the denominators begins: 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 3, 2, 5, 3, 7, 4, ... 1, 3, 1, 5, 3, 7, 2, 9, ... 1, 2, 5, 1, 7, 4, 3, 5, ... 1, 5, 3, 7, 1, 9, 5, 11, ... 1, 3, 7, 4, 9, 1, 11, 6, ... 1, 7, 2, 3, 5, 11, 1, 13, ... 1, 4, 9, 5, 11, 6, 13, 1, ... ...
Links
- Stefano Spezia, First 151 antidiagonals of the array
Crossrefs
Programs
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Mathematica
A[0,0]=1; A[n_,k_]:=Denominator[(FromDigits[Reverse[IntegerDigits[n]]]-k)/(n+k)]; Table[A[n-k,k],{n,0,12},{k,0,n}]//Flatten
Comments