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A022440
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a(n) = c(n-1) + c(n-3) where c is the sequence of positive numbers not in a.
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2
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3, 4, 5, 7, 10, 15, 19, 21, 24, 26, 29, 31, 34, 37, 40, 43, 47, 50, 53, 57, 60, 63, 67, 69, 73, 75, 79, 81, 85, 87, 90, 93, 95, 99, 101, 105, 107, 110, 113, 115, 119, 121, 125, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 179, 181
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OFFSET
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1,1
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COMMENTS
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From N. J. A. Sloane, Nov 24 2004: I'm not sure of the minimal hypotheses needed to generate this sequence, but one method that works is the following:
Start with a(1)=3, a(2)=4, a(3)=5, so that we know c(1)=1 and c(2)=2. Let c(3) = x >= 6, so that a(4) = 1+x >= 6 and x=6 is forced, with a(4)=7. Then c(4) >= 8, a(5) >= 10, so definitely c(4)=8 and c(5)=9. From now on the sequence extends easily.
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LINKS
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MATHEMATICA
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Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 2}]]] &, {3, 4, 5}, Range[59]] (* Ivan Neretin, Mar 30 2017 *)
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CROSSREFS
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Cf. A022424 and references therein.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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