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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.
3
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
0,8
COMMENTS
This array generalizes A367728.
LINKS
FORMULA
A(1, n) = A026741(n+1).
A(2, n) = A060819(n+2).
A(3, n) = A060789(n+3).
A(4, n) = A106609(n+4).
A(5, n) = A106611(n+5).
A(6, n) = A051724(n+6).
A(7, n) = A106615(n+7).
A(8, n) = A106617(n+8) = A231190(n+16).
A(9, n) = A106619(n+9).
A(10, n) = A106612(n+10).
EXAMPLE
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, ...
...
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
CROSSREFS
Cf. A367824 (numerator), A367827 (antidiagonal sums).
Sequence in context: A285117 A135910 A255916 * A107333 A161642 A152141
KEYWORD
nonn,base,frac,tabl
AUTHOR
Stefano Spezia, Dec 02 2023
STATUS
approved