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A064866
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Write numbers 1, then 1 up to 2^2, then 1 up to 3^2, then 1 up to 4^2 and so on.
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9
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1, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
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OFFSET
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1,3
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COMMENTS
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This is a fractal sequence: if the first instance of each number is deleted, the original sequence is recovered. - Franklin T. Adams-Watters, Dec 14 2013
When sequence fills a triangular array by rows, the main diagonal is A064865:
This triangle begins:
....1
...1.2
..3.4.1
.2.3.4.5
6.7.8.9.1
A more natural way of organizing this sequence is as an irregular table consisting of successively larger square matrices:
1;
1, 2;
3, 4;
1, 2, 3;
4, 5, 6;
7, 8, 9;
1, 2, 3, 4;
5, 6, 7, 8;
9,10,11,12;
13,14,15,16;
etc.
(End)
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LINKS
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FORMULA
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For 1 <= n <= 650, a(n) = n - t(t-1)(2t-1)/6, where t = floor((3*n)^(1/3)+1/2). - Mikael Aaltonen, Jan 17 2015
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MATHEMATICA
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PROG
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(PARI) A064866_vec(N=9)=concat(vector(N, i, vector(i^2, j, j))) \\ Note: This creates a vector; use A064866_vec()[n] to get the n-th term. - M. F. Hasler, Feb 17 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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