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A317687 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms is 3-smooth (A003586). 1
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)
OFFSET

1,2

COMMENTS

The 2-smooth variant of this sequence, say b, satisfies b(n) = A001045(n+1) for any n > 0.

LINKS

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

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(C++) See Links section.

CROSSREFS

Cf. A001045, A003586.

Sequence in context: A060120 A065183 A119791 * A026257 A099520 A327432

Adjacent sequences:  A317684 A317685 A317686 * A317688 A317689 A317690

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Aug 04 2018

STATUS

approved

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Last modified May 23 13:45 EDT 2022. Contains 353975 sequences. (Running on oeis4.)