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Search: id:A024431
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| A024431 |
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A generalized difference set on the set of all integers. |
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+0
6
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| 1, 2, 6, 8, 18, 21, 44, 52, 106, 115, 232, 243, 488, 502, 1006, 1024, 2050, 2071, 4144, 4166, 8334, 8358, 16718, 16743, 33488, 33515, 67032, 67060, 134122, 134151, 268304, 268334, 536670, 536702, 1073406, 1073439, 2146880, 2146915, 4293832
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In the set of all positive differences of the sequence each integer appears exactly once, i.e. lambda = 1.
a(A115406(n))-a(A115407(n))=n; a(m)-a(n)=A115409(m*(m-1)/2+n+1), 1<=n<m. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 22 2006
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REFERENCES
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T. Baginova, R. Jajcay, Notes on subtractive properties of natural numbers, Bulletin of the ICA, Vol. 25(1999), pp. 29-40
O. Grosek, R. Jajcay, Generalized Difference Sets on an Infinite Cyclic Semigroup, JCMCC, Vol. 13 (1993), pp. 167-174.
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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 not of form x-y for x, y in N_i, x>y. Union of all N_i gives sequence.
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CROSSREFS
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Cf. A049399.
Cf. A115408, A115409.
Adjacent sequences: A024428 A024429 A024430 this_sequence A024432 A024433 A024434
Sequence in context: A137848 A053355 A005823 this_sequence A053658 A032393 A102656
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KEYWORD
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nonn,nice,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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More terms from Larry Reeves (larryr(AT)acm.org), May 04 2000
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