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A327460
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Lexicographically earliest infinite sequence of distinct positive integers such that for every k >= 1, all the k(k+1)/2 numbers in the triangle of differences of the first k terms are distinct.
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15
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1, 3, 9, 5, 12, 10, 23, 8, 22, 17, 42, 16, 43, 20, 38, 26, 45, 32, 65, 28, 64, 39, 76, 34, 81, 48, 98, 40, 92, 54, 109, 60, 116, 51, 114, 58, 117, 70, 136, 67, 135, 71, 145, 72, 147, 69, 146, 80, 164, 87, 166, 82, 170, 108, 198, 101
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OFFSET
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1,2
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COMMENTS
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This is an infinite version of A327762. The first 55 terms are the same as in A327762.
The usual topological arguments show that there IS a sequence satisfying the definition. So far, the terms of A327460 lie on two roughly straight lines, of slopes about 1.75 and 3.5: see A328069, A328070. - N. J. A. Sloane, Oct 07 2019
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LINKS
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EXAMPLE
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The difference triangle of the first k=8 terms of the sequence is
1, 3, 9, 5, 12, 10, 23, 8, ...
2, 6, -4, 7, -2, 13, -15, ...
4, -10, 11, -9, 15, -28, ...
-14, 21, -20, 24, -43, ...
35, -41, 44, -67, ...
-76, 85, -111, ...
161, -196, ...
-357, ...
All 8*9/2 = 36 numbers are distinct.
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CROSSREFS
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The inverse binomial transform is A327459.
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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