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Search: id:A101274
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| A101274 |
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a(1)=1; for n>1, a(n) is the smallest positive integer such that the set of all sums of adjacent elements up to and including a(n) contains no number more than once. |
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+0
1
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| 1, 2, 4, 5, 8, 10, 14, 21, 15, 16, 26, 25, 34, 22, 48, 38, 71, 40, 74, 90, 28, 69, 113, 47, 94, 54, 46, 143, 153, 83, 128, 49, 249, 75, 133, 225, 125, 131, 270, 145, 230
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does the sequence together with the sums of adjacent elements include all positive integers? Choosing starting values other than a(1)=1 gives other sequences. We could ask, for a given n, which such sequences have the smallest sum of a(k) from k=1 to n.
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EXAMPLE
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a(8)=21 because the set of sums of adjacent elements to this point, call it s(7) is {1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,18,19,20,23,24,27,29,30,32,37,41,43,44}.
The first number missing from this list is 15, but a(8) cannot equal 15 because 15+14=29 and 29 is already in s(7). Similarly a(8) cannot be 16 because 16+14=30.
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CROSSREFS
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Adjacent sequences: A101271 A101272 A101273 this_sequence A101275 A101276 A101277
Sequence in context: A067941 A092265 A163295 this_sequence A080222 A050539 A039895
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KEYWORD
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nonn
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AUTHOR
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David S Newman (DavidSNewman(AT)hotmail.com), Dec 20 2004
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