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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 natural numbers and remove any k's for which S(k) merges with an S(m) with m < k. This sequence gives conjectural values for the remaining k's.
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14
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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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