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A317687
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Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms is 3-smooth (A003586).
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1
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1, 2, 4, 5, 3, 6, 10, 8, 16, 11, 7, 9, 15, 12, 20, 28, 26, 22, 14, 13, 19, 17, 31, 23, 25, 29, 35, 37, 27, 21, 33, 39, 42, 30, 18, 36, 45, 51, 57, 24, 40, 32, 49, 47, 34, 38, 43, 53, 55, 41, 67, 61, 83, 79, 65, 63, 81, 111, 105, 87, 75, 69, 59, 85, 77, 115
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The 2-smooth variant of this sequence, say b, satisfies b(n) = A001045(n+1) for any n > 0.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 6500000 terms
Rémy Sigrist, C++ program for A317687
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EXAMPLE
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The first terms, alongside a(n) + a(n+1), are:
n a(n) a(n) + a(n+1)
-- ---- -------------
1 1 3
2 2 2 * 3
3 4 3^2
4 5 2^3
5 3 3^2
6 6 2^4
7 10 2 * 3^2
8 8 2^3 * 3
9 16 3^3
10 11 2 * 3^2
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MATHEMATICA
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Nest[Append[#, Block[{k = 2}, While[Nand[FreeQ[#, k], SubsetQ[{2, 3}, FactorInteger[k + #[[-1]] ][[All, 1]]]], k++]; k]] &, {1}, 65] (* Michael De Vlieger, Aug 05 2018 *)
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PROG
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(C++) See Links section.
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CROSSREFS
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Cf. A001045, A003586.
Sequence in context: A060120 A065183 A119791 * A026257 A099520 A327432
Adjacent sequences: A317684 A317685 A317686 * A317688 A317689 A317690
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, Aug 04 2018
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STATUS
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approved
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