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Search: id:A092944
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| A092944 |
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Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product +1 is prime. Sequence contains the first member of the groups. |
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+0
4
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| 2, 1, 3, 5, 11, 15, 20, 27, 36, 44, 54, 64, 76, 89, 102, 117, 132, 149, 166, 184, 204, 228, 249, 272, 296, 323, 349, 376, 403, 432, 461, 493, 524, 556, 589, 625, 660, 697, 737, 775, 814, 855, 898, 943, 987, 1031, 1076, 1122, 1169, 1219, 1269, 1321, 1373, 1427
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The n-th group is selected such that it is lexicographically minimal.
First n-2 numbers are the least previously unused numbers.
The (n-1)st number is chosen with the additional condition that if the product is odd, the sum is also odd (to avoid an impossible situation in picking the n-th number).
The n-th number is chosen as the least unused number that meets the two prime conditions.
In the 3rd group, 6 is selectd as the 2nd number rather than 5, else no 3rd number could be found to meet the prime conditions.
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EXAMPLE
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Table begins:
2
1,4
3,6,10
5,7,8,9
11,12,13,14,23
15,16,17,18,19,28
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CROSSREFS
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Cf. A092945, A092946, A092947.
Sequence in context: A070168 A021828 A094341 this_sequence A049902 A096631 A096871
Adjacent sequences: A092941 A092942 A092943 this_sequence A092945 A092946 A092947
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 23 2004
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EXTENSIONS
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Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 07 2008
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