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A134162
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Let S(k) be the sequence s() defined by s(1) = k; for i > 1, s(i) = s(i-1) + gcd(s(i-1), i). Start with the list of positive integers and remove any k's for which S(k) merges with an S(m) with m < k. Each value k > 1 is conjectural.
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16
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1, 2, 4, 8, 16, 20, 44, 92, 110, 136, 152, 170, 172, 188, 200, 212, 236, 242, 256, 272, 316, 332, 368, 440, 488, 500, 590, 616, 620, 632, 650, 676, 704, 710, 742, 788, 824, 848, 892, 946, 952, 968, 1010, 1034, 1036, 1052, 1058, 1088, 1118
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OFFSET
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1,2
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COMMENTS
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For the given initial values k, it is conjectural that their sequences S(k) never merge. The S(k) have been checked to be distinct for 2^60 terms (see Rowland link), but it is possible that they merge later on.
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LINKS
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EXAMPLE
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S(1) = A000027 is the positive integers.
S(2) = [2,4,5,...,i+2,...].
S(3) = [3,4,5,...,i+2,...] merges with S(2) at index 2.
S(4) = [4,6,9,10,15,18,19,20,21,22,33,...] = A084662.
S(5) = [5,6,9,...] = A134736 merges with S(4) at index 2.
(End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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