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A049399
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A generalized difference set on the set of all integers (lambda = 2).
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2
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1, 2, 6, 7, 16, 18, 38, 40, 82, 85, 172, 175, 352, 356, 714, 720, 1442, 1449, 2900, 2907, 5816, 5824, 11650, 11658, 23318, 23327, 46656, 46666, 93334, 93345, 186692, 186704, 373410, 373423, 746848, 746861, 1493724, 1493738, 2987478, 2987493, 5974988, 5975004
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OFFSET
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0,2
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COMMENTS
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In the set of all positive differences of the sequence each integer appears exactly twice, i.e., lambda = 2.
One could try to greedily build such a difference set as follows: b(1) = 1, b(n+1) = b(n)+j with j the smallest difference yet to appear twice. This would begin with {1, 2, 3, 5, 8, 12, 17, 23, 31, 39, 49} and fail; the smallest difference yet to appear twice is then 12 = 17-5, but 49+12 = 61 and 61-39 = 22 = 23-1 = 39-17. - Danny Rorabaugh, Sep 27 2015
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LINKS
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FORMULA
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Let N_1={1, 2}. Given N_i, let N_{i+1} = N_i union {2k+2, 2k+2+j} where k = max element of N_i and j = smallest number of form x-y for at most one pair x, y in N_i, x>y. Union of all N_i gives sequence. - Danny Rorabaugh (mirroring formula in A024431), Sep 27 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Otokar Grosek (grosek(AT)elf.stuba.sk)
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EXTENSIONS
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STATUS
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approved
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