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A283681
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Unique sequence with a(1)=1, a(2)=2, representing an array read by antidiagonals in which the i-th row is this sequence itself multiplied by i.
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5
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1, 2, 2, 2, 4, 3, 2, 4, 6, 4, 4, 4, 6, 8, 5, 3, 8, 6, 8, 10, 6, 2, 6, 12, 8, 10, 12, 7, 4, 4, 9, 16, 10, 12, 14, 8, 6, 8, 6, 12, 20, 12, 14, 16, 9, 4, 12, 12, 8, 15, 24, 14, 16, 18, 10, 4, 8, 18, 16, 10, 18, 28, 16, 18, 20, 11, 4, 8, 12, 24, 20, 12, 21, 32, 18, 20, 22, 12, 6, 8
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OFFSET
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1,2
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COMMENTS
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Any integer greater than 1 appears infinitely many times.
In particular, any n appears at the position (n^2 + n)/2. For prime n > 2, this is its first appearance; for composite n, it is not the first.
2 appears at the positions 2, 3, 4, 7, 22, 232, 26797, ... (A007501(n) + 1).
When the sequence is considered as an array, any prime n appears only in the first row (infinitely many times) and in the first column (once).
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LINKS
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FORMULA
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a((n^2+n)/2)=n.
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EXAMPLE
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The sequence begins: 1, 2, 2, 2, 4, 3, 2, 4, 6, 4, ...
It represents a rectangular array read by downward antidiagonals. The first row of the array is this very sequence itself. The second row is this sequence multiplied by 2, and so on:
1 2 2 2 4 3 ...
2 4 4 4 8 ...
3 6 6 6 ...
4 8 8 ...
5 10 ...
6 ...
...
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MATHEMATICA
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Nest[Flatten@Table[#[[n - i]]*i, {n, Length[#] + 1}, {i, n - 1}] &, {1, 2}, 4]
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CROSSREFS
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Cf. A007501 (number of terms produced by the Mathematica code after n iterations).
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KEYWORD
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AUTHOR
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STATUS
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approved
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